Stochastic Processes and their Applications最新文献

{"title":"Perpetuities with light tails and the local dependence measure","authors":"Julia Le Bihan,&nbsp;Bartosz Kołodziejek","doi":"10.1016/j.spa.2025.104740","DOIUrl":"10.1016/j.spa.2025.104740","url":null,"abstract":"<div><div>This work investigates the tail behavior of solutions to the affine stochastic fixed-point equation of the form <span><math><mrow><mi>X</mi><mover><mrow><mo>=</mo></mrow><mrow><mrow><mi>d</mi></mrow></mrow></mover><mi>A</mi><mi>X</mi><mo>+</mo><mi>B</mi></mrow></math></span>, where <span><math><mi>X</mi></math></span> and <span><math><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></math></span> are independent. Focusing on the light-tail regime, following (Burdzy et al., 2022), we introduce a local dependence measure along with an associated Legendre-type transform. These tools allow us to effectively describe the logarithmic right-tail asymptotics of the solution <span><math><mi>X</mi></math></span>.</div><div>Moreover, we extend our analysis to a related recursive sequence <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>, where <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>n</mi></mrow></msub></math></span> are i.i.d. copies of <span><math><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></math></span>. For this sequence, we construct deterministic scaling <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>n</mi></mrow></msub></math></span> such that <span><math><mrow><msub><mrow><mo>lim sup</mo></mrow><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>/</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> is a.s. positive and finite, with its non-random explicit value provided.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104740"},"PeriodicalIF":1.1,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655317","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":"Uniform bounds for robust mean estimators","authors":"Stanislav Minsker","doi":"10.1016/j.spa.2025.104724","DOIUrl":"10.1016/j.spa.2025.104724","url":null,"abstract":"<div><div>We study estimators of the means of a family of random variables <span><math><mrow><mo>{</mo><mi>f</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>f</mi><mo>∈</mo><mi>F</mi><mo>}</mo></mrow></math></span> that admit uniform, over the class <span><math><mi>F</mi></math></span> of real-valued functions, non-asymptotic error bounds under minimal moment assumptions on the underlying distribution. We show that known robust methods, such as the median-of-means and Catoni’s estimators, can often be viewed as special cases of our construction. The paper’s primary contribution lies in establishing uniform bounds for the deviations of stochastic processes defined by the proposed estimators. Furthermore, we analyze the stability of these estimators within the context of the ‘adversarial contamination’ framework. Finally, we demonstrate the applicability of our methods to the problem of robust multivariate mean estimation, showing that the resulting inequalities achieve optimal dependence on the parameters of the problem.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104724"},"PeriodicalIF":1.1,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655315","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":"Adaptive nonparametric drift estimation for multivariate jump diffusions under sup-norm risk","authors":"Niklas Dexheimer","doi":"10.1016/j.spa.2025.104741","DOIUrl":"10.1016/j.spa.2025.104741","url":null,"abstract":"<div><div>We investigate nonparametric drift estimation for multidimensional jump diffusions based on continuous observations. The results are derived under anisotropic smoothness assumptions and the estimators’ performance is measured in terms of the <span><math><mo>sup</mo></math></span>-norm loss. We present two different Nadaraya–Watson type estimators, which are both shown to achieve the minimax optimal classical nonparametric rate of convergence under varying assumptions on the jump measure. Fully data-driven versions of both estimators are also introduced and shown to attain the same rate of convergence. The results rely on novel uniform moment bounds for empirical processes associated to the investigated jump diffusion, which are of independent interest.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104741"},"PeriodicalIF":1.1,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655314","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 “Large Deviations for Generalized Polya urns with arbitrary Urn Function” [Stochastic Processes and their Applications 127 (2017) 3372 – 3411]","authors":"Simone Franchini","doi":"10.1016/j.spa.2025.104745","DOIUrl":"10.1016/j.spa.2025.104745","url":null,"abstract":"<div><div>We find and correct a mistake in the formulas for the cumulant generating function <span><math><mi>ψ</mi></math></span> of the linear urn problem that are given in the Corollary 12 of Franchini (2017), and its proof. In particular, the correct function <span><math><msub><mrow><mi>ψ</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span> is as follows: <span><span><span><math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>ψ</mi></mrow><mrow><mo>+</mo></mrow></msub><mfenced><mrow><mi>λ</mi><mo>;</mo><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></mfenced></mrow></msup><mo>=</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><msup><mrow><mi>e</mi></mrow><mrow><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mi>λ</mi></mrow></msup><msup><mrow><mfenced><mrow><mn>1</mn><mo>−</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msup></mrow></mfenced></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac></mrow></msup><mi>B</mi><mfenced><mrow><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>b</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac><mo>;</mo><mn>1</mn><mo>−</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msup><mo>,</mo><mn>1</mn></mrow></mfenced></mrow></math></span></span></span>for the positive branch <span><math><mrow><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><span><span><math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>ψ</mi></mrow><mrow><mo>+</mo></mrow></msub><mfenced><mrow><mi>λ</mi><mo>;</mo><mi>b</mi><mo>&lt;</mo><mn>0</mn></mrow></mfenced></mrow></msup><mo>=</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><msup><mrow><mi>e</mi></mrow><mrow><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mi>λ</mi></mrow></msup><msup><mrow><mfenced><mrow><mn>1</mn><mo>−</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msup></mrow></mfenced></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac></mrow></msup><mi>B</mi><mfenced><mrow><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mi>b</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>b</mi></mrow></mfrac><mo>;</mo><mn>0</mn><mo>,</mo><mspace></mspace><mn>1</mn><mo>−</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>λ</mi></mrow></msup></mrow></mfenced></mrow></math></span></span></span>for the negative branch <span><math><mrow><mi>b</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>. We remark that this issue does not affect the main result, nor any other finding of the paper. We also correct a minor typo in the proof of Theorem 9.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104745"},"PeriodicalIF":1.2,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094594","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":"Weak Error on the densities for the Euler scheme of stable additive SDEs with Hölder drift","authors":"Mathis Fitoussi,&nbsp;Stéphane Menozzi","doi":"10.1016/j.spa.2025.104736","DOIUrl":"10.1016/j.spa.2025.104736","url":null,"abstract":"<div><div>We are interested in the Euler–Maruyama discretization of the SDE <span><span><span><math><mrow><mspace></mspace><mi>d</mi><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>b</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mspace></mspace><mi>d</mi><mi>t</mi><mo>+</mo><mspace></mspace><mi>d</mi><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo></mrow></math></span></span></span>where <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> is a symmetric isotropic <span><math><mi>d</mi></math></span>-dimensional <span><math><mi>α</mi></math></span>-stable process, <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></mrow></math></span> and the drift <span><math><mrow><mi>b</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mfenced><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>,</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>β</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></mfenced></mrow></math></span>, <span><math><mrow><mi>β</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, is bounded and Hölder regular in space. Using an Euler scheme with a randomization of the time variable, we show that, denoting <span><math><mrow><mi>γ</mi><mo>≔</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>−</mo><mn>1</mn></mrow></math></span>, the weak error on densities related to this discretization converges at the rate <span><math><mrow><mi>γ</mi><mo>/</mo><mi>α</mi></mrow></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104736"},"PeriodicalIF":1.1,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655380","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":"Birth-death processes are time-changed Feller’s Brownian motions","authors":"Liping Li","doi":"10.1016/j.spa.2025.104738","DOIUrl":"10.1016/j.spa.2025.104738","url":null,"abstract":"&lt;div&gt;&lt;div&gt;A Feller’s Brownian motion refers to a Feller process on the interval &lt;span&gt;&lt;math&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;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; that is equivalent to the killed Brownian motion before reaching 0. It is fully determined by four parameters &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, reflecting its killing, reflecting, sojourn, and jumping behaviors at the boundary 0. On the other hand, a birth–death process is a continuous-time Markov chain on &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with a given birth–death &lt;span&gt;&lt;math&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-matrix, and it is characterized by three parameters &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; that describe its killing, reflecting, and jumping behaviors at the boundary &lt;span&gt;&lt;math&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The primary objective of this paper is to establish a connection between Feller’s Brownian motion and birth–death process. We will demonstrate that any Feller’s Brownian motion can be transformed into a specific birth–death process through a unique time change transformation, and conversely, any birth–death process can be derived from Feller’s Brownian motion via time change. Specifically, the birth–death process generated by the Feller’s Brownian motion, determined by the parameters &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, through time change, has the parameters: &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&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;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ν&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&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;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&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;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a sequence derived by allocating weights to the measure &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; in a specific manner. Utilizing the pathwise representation of Feller’s Brownian motion, our results provide a pathwise construction scheme for birth–death processes, addressing a gap in the existing lite","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104738"},"PeriodicalIF":1.1,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655316","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":"The phase transition of the voter model on evolving scale-free networks","authors":"John Fernley","doi":"10.1016/j.spa.2025.104737","DOIUrl":"10.1016/j.spa.2025.104737","url":null,"abstract":"<div><div>The voter model on a social network can explain consensus formation, where real networks feature a heterogeneous degree distribution and also change in time. We study the voter model in an environment with both features: a rank one scale-free network evolving in time by each vertex updating its edge neighbourhood at rate <span><math><mi>κ</mi></math></span>.</div><div>When <span><math><mrow><mi>κ</mi><mo>≫</mo><mn>1</mn></mrow></math></span> the dynamic giant has no effect up to a polylogarithmic correction, but for more slowly changing graphs consensus takes <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>κ</mi></mrow></mfrac></math></span> longer without a dynamic giant. This continues until <span><math><mrow><mi>κ</mi><mo>≪</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac></mrow></math></span>, where this factor <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>κ</mi></mrow></mfrac></math></span> becomes <span><math><mfrac><mrow><mi>N</mi></mrow><mrow><mo>log</mo><mi>N</mi></mrow></mfrac></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104737"},"PeriodicalIF":1.1,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655377","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":"Nonlinear Graphon mean-field systems","authors":"Fabio Coppini ,&nbsp;Anna De Crescenzo ,&nbsp;Huyên Pham","doi":"10.1016/j.spa.2025.104728","DOIUrl":"10.1016/j.spa.2025.104728","url":null,"abstract":"<div><div>We address a system of weakly interacting particles where the heterogeneous connections among the particles are described by a graph sequence and the number of particles grows to infinity. Our results extend the existing law of large numbers and propagation of chaos results to the case where the interaction between one particle and its neighbours is expressed as a nonlinear function of the local empirical measure. In the limit of the number of particles which tends to infinity, if the graph sequence converges to a graphon, then we show that the limit system is described by an infinite collection of processes and can be seen as a process in a suitable <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> space constructed via a Fubini extension. The proof is built on decoupling techniques and careful estimates of the Wasserstein distance.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104728"},"PeriodicalIF":1.1,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655313","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-normalized partial sums of heavy-tailed time series","authors":"Muneya Matsui ,&nbsp;Thomas Mikosch ,&nbsp;Olivier Wintenberger","doi":"10.1016/j.spa.2025.104729","DOIUrl":"10.1016/j.spa.2025.104729","url":null,"abstract":"<div><div>We study the joint limit behavior of sums, maxima and <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-type moduli for samples taken from an <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>-valued regularly varying stationary sequence with infinite variance. As a consequence, we can determine the distributional limits for ratios of sums and maxima, studentized sums, and other self-normalized quantities in terms of hybrid characteristic-distribution functions and Laplace transforms. These transforms enable one to calculate moments of the limits and to characterize the differences between the iid and stationary cases in terms of indices which describe effects of extremal clustering on functionals acting on the dependent sequence.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104729"},"PeriodicalIF":1.1,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144563183","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":"A complete characterization of monotonicity equivalence for continuous-time Markov processes","authors":"Motoya Machida","doi":"10.1016/j.spa.2025.104735","DOIUrl":"10.1016/j.spa.2025.104735","url":null,"abstract":"<div><div>Dai Pra et al., studied two notions of monotonicity for continuous-time Markov processes on a finite partially ordered set (poset). They conjectured that monotonicity equivalence holds for a poset of W-glued diamond, and that there is no other case when it has no acyclic extension. We proved their conjecture and were able to provide a complete characterization of posets for monotonicity equivalence.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104735"},"PeriodicalIF":1.1,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653071","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}