Stochastic Processes and their Applications最新文献

{"title":"Profile cut-off phenomenon for the ergodic Feller root process","authors":"Gerardo Barrera ,&nbsp;Liliana Esquivel","doi":"10.1016/j.spa.2025.104587","DOIUrl":"10.1016/j.spa.2025.104587","url":null,"abstract":"<div><div>The present manuscript is devoted to the study of the convergence to equilibrium as the noise intensity <span><math><mrow><mi>ɛ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> tends to zero for ergodic random systems out of equilibrium driven by multiplicative non-linear noise of the type <span><span><span><math><mrow><mi>d</mi><msubsup><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>ɛ</mi></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mi>b</mi><mo>−</mo><mi>a</mi><msubsup><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>ɛ</mi></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow><mi>d</mi><mi>t</mi><mo>+</mo><mi>ɛ</mi><msqrt><mrow><msubsup><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>ɛ</mi></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></msqrt><mi>d</mi><msub><mrow><mi>B</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mspace></mspace><msubsup><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>ɛ</mi></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>x</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>⩾</mo><mn>0</mn><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>x</mi><mo>⩾</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> are constants, and <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>⩾</mo><mn>0</mn></mrow></msub></math></span> is a one dimensional standard Brownian motion. More precisely, we show the strongest notion of asymptotic profile cut-off phenomenon in the total variation distance and in the renormalized Wasserstein distance when <span><math><mi>ɛ</mi></math></span> tends to zero with explicit cut-off time, explicit time window, and explicit profile function. In addition, asymptotics of the so-called mixing times are given explicitly.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104587"},"PeriodicalIF":1.1,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143262160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Growth condition on the generator of BSDE with singular terminal value ensuring continuity up to terminal time","authors":"Dorian Cacitti-Holland,&nbsp;Laurent Denis,&nbsp;Alexandre Popier","doi":"10.1016/j.spa.2025.104588","DOIUrl":"10.1016/j.spa.2025.104588","url":null,"abstract":"<div><div>We study the limit behavior of the solution of a backward stochastic differential equation when the terminal condition is singular, that is it can be equal to infinity with a positive probability. In the Markovian setting, Malliavin’s calculus enables us to prove continuity if a balance condition between the growth w.r.t. <span><math><mi>y</mi></math></span> and the growth w.r.t. <span><math><mi>z</mi></math></span> of the generator is satisfied. As far as we know, this condition is new. We apply our result to liquidity problem in finance and to the solution of some semi-linear partial differential equation ; the imposed assumption is also new in the literature on PDE.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104588"},"PeriodicalIF":1.1,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143262159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Self-switching random walks on Erdös–Rényi random graphs feel the phase transition","authors":"G. Iacobelli ,&nbsp;G. Ost ,&nbsp;D.Y. Takahashi","doi":"10.1016/j.spa.2025.104589","DOIUrl":"10.1016/j.spa.2025.104589","url":null,"abstract":"<div><div>We study random walks on Erdös–Rényi random graphs in which, every time the random walk returns to the starting point, first an edge probability is independently sampled according to a priori measure <span><math><mi>μ</mi></math></span>, and then an Erdös–Rényi random graph is sampled according to that edge probability. When the edge probability <span><math><mi>p</mi></math></span> does not depend on the size of the graph <span><math><mi>n</mi></math></span> (dense case), we show that the proportion of time the random walk spends on different values of <span><math><mi>p</mi></math></span> – <em>occupation measure</em> – converges to the a priori measure <span><math><mi>μ</mi></math></span> as <span><math><mi>n</mi></math></span> goes to infinity. More interestingly, when <span><math><mrow><mi>p</mi><mo>=</mo><mi>λ</mi><mo>/</mo><mi>n</mi></mrow></math></span> (sparse case), we show that the occupation measure converges to a limiting measure with a density that is a function of the survival probability of a Poisson branching process. This limiting measure is supported on the supercritical values for the Erdös–Rényi random graphs, showing that self-witching random walks can detect the phase transition.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104589"},"PeriodicalIF":1.1,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “Maxima over random time intervals for heavy-tailed compound renewal and Lévy processes” [Stochastic Processes and their Applications 176 (2024) 104422]","authors":"Sergey Foss ,&nbsp;Dmitry Korshunov ,&nbsp;Zbigniew Palmowski","doi":"10.1016/j.spa.2025.104572","DOIUrl":"10.1016/j.spa.2025.104572","url":null,"abstract":"","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104572"},"PeriodicalIF":1.1,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of quasi-stationary distributions for downward skip-free Markov chains","authors":"Kosuke Yamato","doi":"10.1016/j.spa.2025.104579","DOIUrl":"10.1016/j.spa.2025.104579","url":null,"abstract":"<div><div>For downward skip-free continuous-time Markov chains on non-negative integers killed at zero, the existence of the quasi-stationary distribution is studied. The scale function for the process is introduced, and the boundary is classified by a certain integrability condition on the scale function, which gives an extension of Feller’s classification of the boundary for birth-and-death processes. The existence and the set of quasi-stationary distributions are characterized by the scale function and the new classification of the boundary.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104579"},"PeriodicalIF":1.1,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of wandering bumps for Hawkes processes interacting on the circle","authors":"Zoé Agathe-Nerine","doi":"10.1016/j.spa.2025.104577","DOIUrl":"10.1016/j.spa.2025.104577","url":null,"abstract":"<div><div>We consider a population of Hawkes processes modeling the activity of <span><math><mi>N</mi></math></span> interacting neurons. The neurons are regularly positioned on the circle <span><math><mrow><mo>[</mo><mo>−</mo><mi>π</mi><mo>,</mo><mi>π</mi><mo>]</mo></mrow></math></span>, and the connectivity between neurons is given by a cosine kernel. The firing rate function is a sigmoid. The large population limit admits a locally stable manifold of stationary solutions. The main result of the paper concerns the long-time proximity of the synaptic voltage of the population to this manifold in polynomial times in <span><math><mi>N</mi></math></span>. We show in particular that the phase of the voltage along this manifold converges towards a Brownian motion on a time scale of order <span><math><mi>N</mi></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104577"},"PeriodicalIF":1.1,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost sure limit theorems with applications to non-regular continued fraction algorithms","authors":"Claudio Bonanno ,&nbsp;Tanja I. Schindler","doi":"10.1016/j.spa.2025.104573","DOIUrl":"10.1016/j.spa.2025.104573","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider a conservative ergodic measure-preserving transformation &lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of the measure space &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; a &lt;span&gt;&lt;math&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-finite measure and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Given an observable &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, it is well known from results by Aaronson, see Aaronson (1997), that in general the asymptotic behaviour of the Birkhoff sums &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; strongly depends on the point &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and that there exists no sequence &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for which &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-almost every &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. In this paper we consider the case &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;⁄&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and continue the investigation initiated in Bonanno and Schindler (2022). We show that for transformations &lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with strong mixing assumptions for the induced map on a finite measure set, the almost sure asymptotic behaviour of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for an unbounded observable &lt;span&gt;&lt;math&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; may be obtained using two methods, addition to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; of a number of summands depending on &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and trimming. The obtained sums are then asymptotic to a scalar multiple of &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The results are applied to a couple of non-regular continued fraction algorithms, the backward (or Rényi type) continued fraction and the even-integer c","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104573"},"PeriodicalIF":1.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The accumulation of beneficial mutations and convergence to a Poisson process","authors":"Nantawat Udomchatpitak,&nbsp;Jason Schweinsberg","doi":"10.1016/j.spa.2025.104578","DOIUrl":"10.1016/j.spa.2025.104578","url":null,"abstract":"<div><div>We consider a model of a population with fixed size <span><math><mi>N</mi></math></span>, which is subjected to an unlimited supply of beneficial mutations at a constant rate <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span>. Individuals with <span><math><mi>k</mi></math></span> beneficial mutations have the fitness <span><math><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>k</mi></mrow></msup></math></span>. Each individual dies at rate 1 and is replaced by a random individual chosen with probability proportional to its fitness. We show that when <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>≪</mo><mn>1</mn><mo>/</mo><mrow><mo>(</mo><mi>N</mi><mo>log</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mi>η</mi></mrow></msup><mo>≪</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>≪</mo><mn>1</mn></mrow></math></span> for some <span><math><mrow><mi>η</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the fixation times of beneficial mutations, after a time scaling, converge to the times of a Poisson process, even though for some choices of <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> satisfying these conditions, there will sometimes be multiple beneficial mutations with distinct origins in the population, competing against each other.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104578"},"PeriodicalIF":1.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Almost sure approximations and laws of iterated logarithm for signatures","authors":"Yuri Kifer","doi":"10.1016/j.spa.2025.104576","DOIUrl":"10.1016/j.spa.2025.104576","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We obtain strong invariance principles for normalized multiple iterated sums and integrals of the form &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;mo&gt;⋯&lt;/mo&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mo&gt;⋯&lt;/mo&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;mo&gt;⋯&lt;/mo&gt;&lt;mo&gt;⊗&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⋯&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are centered stationary vector processes with some weak dependence properties. These imply also laws of iterated logarithm and an almost sure central limit theorem for such objects. In the continuous time we work both under direct weak dependence assumptions and also within the suspension setup which is more appropriate for applications in dynamical systems. Similar results under substantially more restricted conditions were obtained in Friz and Kifer (2024) relying heavily on rough paths theory and notations while here we obtain these results in a more direct way","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"182 ","pages":"Article 104576"},"PeriodicalIF":1.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143142343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Berry-Esseen bounds for functionals of independent random variables","authors":"Qi-Man Shao ,&nbsp;Zhuo-Song Zhang","doi":"10.1016/j.spa.2025.104574","DOIUrl":"10.1016/j.spa.2025.104574","url":null,"abstract":"<div><div>We develop a new Berry–Esseen bound for functionals of independent random variables by introducing a simple form of Chatterjee’s perturbative approach. The main result is applied to the weighted triangle counts in inhomogeneous random graphs, random field Curie–Weiss model, set approximation with random tessellations and random sphere of influence graph models. The rate of convergence is the best possible.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104574"},"PeriodicalIF":1.1,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}