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Stochastic Processes and their Applications最新文献

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Symmetry and functional inequalities for stable Lévy-type operators
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-02-10 DOI: 10.1016/j.spa.2025.104600
Lu-Jing Huang , Tao Wang
{"title":"Symmetry and functional inequalities for stable Lévy-type operators","authors":"Lu-Jing Huang ,&nbsp;Tao Wang","doi":"10.1016/j.spa.2025.104600","DOIUrl":"10.1016/j.spa.2025.104600","url":null,"abstract":"<div><div>In this paper, we establish the sufficient and necessary conditions for the symmetry of the following stable Lévy-type operator <span><math><mi>L</mi></math></span> on <span><math><mi>R</mi></math></span>: <span><span><span><math><mrow><mi>L</mi><mo>=</mo><mi>a</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mfrac><mrow><mi>d</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo>,</mo></mrow></math></span></span></span>where <span><math><mi>a</mi></math></span> is a continuous and strictly positive function, and <span><math><mi>b</mi></math></span> is a differentiable function. We then study the criteria for functional inequalities, such as logarithmic Sobolev inequalities, Nash inequalities and super-Poincaré inequalities under the assumption of symmetry. Our approach involves the Orlicz space theory and the estimates of the Green functions.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104600"},"PeriodicalIF":1.1,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395378","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}
引用次数: 0
Laws of the iterated and single logarithm for sums of independent indicators, with applications to the Ginibre point process and Karlin’s occupancy scheme
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-02-10 DOI: 10.1016/j.spa.2025.104597
Dariusz Buraczewski , Alexander Iksanov , Valeriya Kotelnikova
{"title":"Laws of the iterated and single logarithm for sums of independent indicators, with applications to the Ginibre point process and Karlin’s occupancy scheme","authors":"Dariusz Buraczewski ,&nbsp;Alexander Iksanov ,&nbsp;Valeriya Kotelnikova","doi":"10.1016/j.spa.2025.104597","DOIUrl":"10.1016/j.spa.2025.104597","url":null,"abstract":"<div><div>We prove a law of the iterated logarithm (LIL) for an infinite sum of independent indicators parameterized by <span><math><mi>t</mi></math></span> and monotone in <span><math><mi>t</mi></math></span> as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span>. It is shown that if the expectation <span><math><mi>b</mi></math></span> and the variance <span><math><mi>a</mi></math></span> of the sum are comparable, then the normalization in the LIL includes the iterated logarithm of <span><math><mi>a</mi></math></span>. If the expectation grows faster than the variance, while the ratio <span><math><mrow><mo>log</mo><mi>b</mi><mo>/</mo><mo>log</mo><mi>a</mi></mrow></math></span> remains bounded, then the normalization in the LIL includes the single logarithm of <span><math><mi>a</mi></math></span> (so that the LIL becomes a law of the single logarithm). Applications of our result are given to the number of points of the infinite Ginibre point process in a disk and the number of occupied boxes and related quantities in Karlin’s occupancy scheme.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104597"},"PeriodicalIF":1.1,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395379","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}
引用次数: 0
Effective growth rates in a periodically changing environment: From mutation to invasion 周期性变化环境中的有效增长率：从突变到入侵
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-02-08 DOI: 10.1016/j.spa.2025.104598
Manuel Esser , Anna Kraut
{"title":"Effective growth rates in a periodically changing environment: From mutation to invasion","authors":"Manuel Esser ,&nbsp;Anna Kraut","doi":"10.1016/j.spa.2025.104598","DOIUrl":"10.1016/j.spa.2025.104598","url":null,"abstract":"<div><div>We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the environment, all of these parameters vary over time as piecewise constant and periodic functions, on an intermediate time-scale between those of stabilisation of the resident population (fast) and exponential growth of mutants (slow). Studying the growth of emergent mutants and their invasion of the resident population in the limit of small mutation rates for a simultaneously diverging population size, we are able to determine their effective growth rates. We describe this growth as a mesoscopic scaling-limit of the orders of population sizes, where we observe an averaging effect of the invasion fitness. Moreover, we prove a limit result for the sequence of consecutive macroscopic resident traits that is similar to the so-called trait-substitution-sequence.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104598"},"PeriodicalIF":1.1,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143528801","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}
引用次数: 0
Wasserstein asymptotics for Brownian motion on the flat torus and Brownian interlacements
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-02-08 DOI: 10.1016/j.spa.2025.104595
Mauro Mariani , Dario Trevisan
{"title":"Wasserstein asymptotics for Brownian motion on the flat torus and Brownian interlacements","authors":"Mauro Mariani ,&nbsp;Dario Trevisan","doi":"10.1016/j.spa.2025.104595","DOIUrl":"10.1016/j.spa.2025.104595","url":null,"abstract":"<div><div>We study the large time behaviour of the optimal transportation cost towards the uniform distribution, for the occupation measure of a stationary Brownian motion on the flat torus in <span><math><mi>d</mi></math></span> dimensions, where the cost of transporting a unit of mass is given by a power of the flat distance. We establish a global upper bound, in terms of the limit for the analogue problem concerning the occupation measure of the Brownian interlacement on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. We conjecture that our bound is sharp and that our techniques may allow for similar studies on a larger variety of problems, e.g. general diffusion processes on weighted Riemannian manifolds.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104595"},"PeriodicalIF":1.1,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377183","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}
引用次数: 0
The contact process on a graph adapting to the infection
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-02-07 DOI: 10.1016/j.spa.2025.104596
John Fernley , Peter Mörters , Marcel Ortgiese
{"title":"The contact process on a graph adapting to the infection","authors":"John Fernley ,&nbsp;Peter Mörters ,&nbsp;Marcel Ortgiese","doi":"10.1016/j.spa.2025.104596","DOIUrl":"10.1016/j.spa.2025.104596","url":null,"abstract":"<div><div>We find a non-trivial phase transition for the contact process, a simple model for infection without immunity, on a network which reacts dynamically to prevent an epidemic. This network is initially blue distributed as an Erdős–Rényi graph, but is made adaptive via updating in only the infected neighbourhoods, at constant rate. Adaptive dynamics are new to the mathematical contact process literature—in adaptive dynamics the presence of infection can help to prevent the spread and thus monotonicity-based techniques fail. We show, further, that the phase transition in the fast adaptive model occurs at larger infection rate than in the non-adaptive model.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104596"},"PeriodicalIF":1.1,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377182","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}
引用次数: 0
On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-02-06 DOI: 10.1016/j.spa.2025.104592
Kaustav Das , Gregory Markowsky , Binghao Wu
{"title":"On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes","authors":"Kaustav Das ,&nbsp;Gregory Markowsky ,&nbsp;Binghao Wu","doi":"10.1016/j.spa.2025.104592","DOIUrl":"10.1016/j.spa.2025.104592","url":null,"abstract":"<div><div>We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes the Brownian motion case. We also discuss related results present in the literature for fractional Brownian motion, and in particular give a counter-example to a result in Guo et al. (2019) related to this question.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104592"},"PeriodicalIF":1.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143360794","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}
引用次数: 0
Poisson approximation of fixed-degree nodes in weighted random connection models
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-02-05 DOI: 10.1016/j.spa.2025.104593
Christian Hirsch , Benedikt Jahnel , Sanjoy Kumar Jhawar , Peter Juhasz
{"title":"Poisson approximation of fixed-degree nodes in weighted random connection models","authors":"Christian Hirsch ,&nbsp;Benedikt Jahnel ,&nbsp;Sanjoy Kumar Jhawar ,&nbsp;Peter Juhasz","doi":"10.1016/j.spa.2025.104593","DOIUrl":"10.1016/j.spa.2025.104593","url":null,"abstract":"<div><div>We present a process-level Poisson-approximation result for the degree-<span><math><mi>k</mi></math></span> vertices in a high-density weighted random connection model with preferential-attachment kernel in a finite-volume Borel set. Our main focus lies on the impact of the left tails of the weight distribution for which we establish general criteria based on their small-weight quantiles. To illustrate that our conditions are broadly applicable, we verify them for weight distributions with polynomial and stretched exponential left tails. The proofs rest on truncation arguments and a recently established quantitative Poisson approximation result for functionals of Poisson point processes.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"183 ","pages":"Article 104593"},"PeriodicalIF":1.1,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143350736","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}
引用次数: 0
Profile cut-off phenomenon for the ergodic Feller root process
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-01-31 DOI: 10.1016/j.spa.2025.104587
Gerardo Barrera , Liliana Esquivel
{"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}
引用次数: 0
Growth condition on the generator of BSDE with singular terminal value ensuring continuity up to terminal time
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-01-31 DOI: 10.1016/j.spa.2025.104588
Dorian Cacitti-Holland, Laurent Denis, Alexandre Popier
{"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}
引用次数: 0
Self-switching random walks on Erdös–Rényi random graphs feel the phase transition
IF 1.1 2区 数学 SCI
Stochastic Processes and their Applications Pub Date : 2025-01-31 DOI: 10.1016/j.spa.2025.104589
G. Iacobelli , G. Ost , D.Y. Takahashi
{"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}
引用次数: 0
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