Stochastic Processes and their Applications最新文献

{"title":"Large deviations for empirical measures of self-interacting Markov chains","authors":"Amarjit Budhiraja ,&nbsp;Adam Waterbury ,&nbsp;Pavlos Zoubouloglou","doi":"10.1016/j.spa.2025.104640","DOIUrl":"10.1016/j.spa.2025.104640","url":null,"abstract":"<div><div>Let <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mi>o</mi></mrow></msup></math></span> be a finite set and, for each probability measure <span><math><mi>m</mi></math></span> on <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mi>o</mi></mrow></msup></math></span>, let <span><math><mrow><mi>G</mi><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></math></span> be a transition kernel on <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mi>o</mi></mrow></msup></math></span>. Consider the sequence <span><math><mrow><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow></math></span> of <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mi>o</mi></mrow></msup></math></span>-valued random variables such that, given <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>, the conditional distribution of <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> is <span><math><mrow><mi>G</mi><mrow><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mi>⋅</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mi>δ</mi></mrow><mrow><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub></mrow></math></span>. Under conditions on <span><math><mi>G</mi></math></span> we establish a large deviation principle for the sequence <span><math><mrow><mo>{</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>}</mo></mrow></math></span>. As one application of this result we obtain large deviation asymptotics for the Aldous et al. (1988) approximation scheme for quasi-stationary distributions of finite state Markov chains. The conditions on <span><math><mi>G</mi></math></span> cover other models as well, including certain models with edge or vertex reinforcement.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104640"},"PeriodicalIF":1.1,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726092","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":"Limit theorems for high-dimensional Betti numbers in the multiparameter random simplicial complexes","authors":"Takashi Owada ,&nbsp;Gennady Samorodnitsky","doi":"10.1016/j.spa.2025.104641","DOIUrl":"10.1016/j.spa.2025.104641","url":null,"abstract":"<div><div>We consider the multiparameter random simplicial complex on a vertex set <span><math><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></math></span>, which is parameterized by multiple connectivity probabilities. Our key results concern the topology of this complex of dimensions higher than the critical dimension. We show that the higher-dimensional Betti numbers satisfy strong laws of large numbers and central limit theorems. Moreover, lower tail large deviations for these Betti numbers are also discussed. Some of our results indicate an occurrence of phase transitions in terms of the scaling constants of the central limit theorem, and the exponentially decaying rate of convergence of lower tail large deviation probabilities.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104641"},"PeriodicalIF":1.1,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726093","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":"Multiple and weak Markov properties in Hilbert spaces with applications to fractional stochastic evolution equations","authors":"Kristin Kirchner ,&nbsp;Joshua Willems","doi":"10.1016/j.spa.2025.104639","DOIUrl":"10.1016/j.spa.2025.104639","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We define a number of higher-order Markov properties for stochastic processes &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&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;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, indexed by an interval &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;T&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; and taking values in a real and separable Hilbert space &lt;span&gt;&lt;math&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. We furthermore investigate the relations between them. In particular, for solutions to the stochastic evolution equation &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̇&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is a linear operator acting on functions mapping from &lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; to &lt;span&gt;&lt;math&gt;&lt;mi&gt;U&lt;/mi&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;mover&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̇&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&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;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is the formal derivative of a &lt;span&gt;&lt;math&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-valued cylindrical Wiener process, we prove necessary and sufficient conditions for the weakest Markov property via locality of the precision operator &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;As an application, we consider the space–time fractional parabolic operator &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; of order &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&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;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a linear operator generating a &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-semigroup on &lt;span&gt;&lt;math&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. We prove that the resulting solution process satisfies an &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;th order Markov property if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&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;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and show that a necessary condition for the weakest Markov property is generally not satisfied if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;∉&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. The relevance of this class of processes is twofold: Firstly, it can be seen as a spatiotemporal generalization of Whittle–Matérn Gaussian random fields if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&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;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for a spatial domain &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104639"},"PeriodicalIF":1.1,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761207","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":"Harmonizable Multifractional Stable Field: Sharp results on sample path behavior","authors":"Antoine Ayache,&nbsp;Christophe Louckx","doi":"10.1016/j.spa.2025.104638","DOIUrl":"10.1016/j.spa.2025.104638","url":null,"abstract":"<div><div>For about three decades now, there is an increasing interest in study of multifractional processes/fields. The paradigmatic example of them is Multifractional Brownian Field (MBF) over <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, which is a Gaussian generalization with varying Hurst parameter (the Hurst function) of the well-known Fractional Brownian Motion (FBM). Harmonizable Multifractional Stable Field (HMSF) is a very natural (and maybe the most natural) extension of MBF to the framework of heavy-tailed Symmetric <span><math><mi>α</mi></math></span>-Stable (S<span><math><mi>α</mi></math></span>S) distributions. Many methods related with Gaussian fields fail to work in such a non-Gaussian framework, this is what makes study of HMSF to be difficult. In our article we construct wavelet type random series representations for the S<span><math><mi>α</mi></math></span>S stochastic field generating HMSF and for related fields. Then, under weakened versions of the usual Hölder condition on the Hurst function, we obtain sharp results on sample path behavior of HMSF: optimal global and pointwise moduli of continuity, quasi-optimal pointwise modulus of continuity on a universal event of probability 1 not depending on the location, and an estimate of the behavior at infinity which is optimal when the Hurst function has a limit at infinity to which it converges at a logarithmic rate.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"186 ","pages":"Article 104638"},"PeriodicalIF":1.1,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734909","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 lower bound for pc in range-R bond percolation in four, five and six dimensions","authors":"Jieliang Hong","doi":"10.1016/j.spa.2025.104637","DOIUrl":"10.1016/j.spa.2025.104637","url":null,"abstract":"<div><div>For the range-<span><math><mi>R</mi></math></span> bond percolation in <span><math><mrow><mi>d</mi><mo>=</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn></mrow></math></span>, we obtain a lower bound for the critical probability <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> for <span><math><mi>R</mi></math></span> large, agreeing with the conjectured asymptotics and thus complementing the corresponding results of Van der Hofstad and Sakai (2005) for <span><math><mrow><mi>d</mi><mo>&gt;</mo><mn>6</mn></mrow></math></span>, and Frei and Perkins (2016), Hong (2023) for <span><math><mrow><mi>d</mi><mo>≤</mo><mn>3</mn></mrow></math></span>. The lower bound proof is completed by showing the extinction of the associated SIR epidemic model. To prove the extinction of the SIR epidemics, we introduce a refined model of the branching random walk, called a self-avoiding branching random walk, whose total range dominates that of the SIR epidemic process.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104637"},"PeriodicalIF":1.1,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685653","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":"Convergence of the open WASEP stationary measure without Liggett’s condition","authors":"Zoe Himwich","doi":"10.1016/j.spa.2025.104634","DOIUrl":"10.1016/j.spa.2025.104634","url":null,"abstract":"<div><div>We demonstrate that Liggett’s condition can be relaxed without disrupting the convergence of open ASEP stationary measures to the open KPZ stationary measure. This is equivalent to demonstrating that, under weak asymmetry scaling and appropriate scaling of time and space, the four-parameter Askey–Wilson process converges to a two-parameter continuous dual Hahn process. We conjecture that the convergence of the open ASEP height function process to solutions to the open KPZ equation will hold for a wider range of ASEP parameters than those permitted by Liggett’s condition.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104634"},"PeriodicalIF":1.1,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685650","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 Benamou–Brenier formula for transport distances between stationary random measures","authors":"Martin Huesmann,&nbsp;Bastian Müller","doi":"10.1016/j.spa.2025.104633","DOIUrl":"10.1016/j.spa.2025.104633","url":null,"abstract":"<div><div>We derive a Benamou–Brenier type dynamical formulation for the Kantorovich–Wasserstein extended metric <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> between stationary random measures recently introduced in Erbar et al., (2024). A key step is a reformulation of the extended metric <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> using Palm probabilities.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104633"},"PeriodicalIF":1.1,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685652","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":"Symmetric KL-divergence by Stein’s method","authors":"Liu-Quan Yao ,&nbsp;Song-Hao Liu","doi":"10.1016/j.spa.2025.104635","DOIUrl":"10.1016/j.spa.2025.104635","url":null,"abstract":"<div><div>In this paper, we consider the symmetric KL-divergence between the sum of independent variables and a Gaussian distribution, and obtain a convergence rate of order <span><math><mrow><mi>O</mi><mfenced><mrow><mfrac><mrow><mo>ln</mo><mi>n</mi></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mfenced></mrow></math></span>. The proof is based on Stein’s method. The convergence rate of order <span><math><mrow><mi>O</mi><mfenced><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt></mrow></mfrac></mrow></mfenced></mrow></math></span> and <span><math><mrow><mi>O</mi><mfenced><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></mfenced></mrow></math></span> are also obtained under higher moment condition.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104635"},"PeriodicalIF":1.1,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685651","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":"Asymptotics for irregularly observed long memory processes","authors":"Mohamedou Ould Haye ,&nbsp;Anne Philippe","doi":"10.1016/j.spa.2025.104631","DOIUrl":"10.1016/j.spa.2025.104631","url":null,"abstract":"<div><div>We study the effect of observing a long-memory stationary process at irregular time points via a renewal process. We establish a sharp difference in the asymptotic behaviour of the self-normalized sample mean of the observed process depending on the renewal process. In particular, we show that if the renewal process has a moderate heavy-tail distribution, then the limit is a so-called Normal Variance Mixture (NVM) and we characterize the randomized variance part of the limiting NVM as an integral function of a Lévy stable motion. Otherwise, the normalized sample mean will be asymptotically normal.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104631"},"PeriodicalIF":1.1,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685649","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":"Partial divisibility of random sets","authors":"Jnaneshwar Baslingker,&nbsp;Biltu Dan","doi":"10.1016/j.spa.2025.104632","DOIUrl":"10.1016/j.spa.2025.104632","url":null,"abstract":"<div><div>In this article, we ask the following question: Let <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> be the void functional of a random closed set <span><math><mi>X</mi></math></span>. For which <span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> is <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>X</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span> a void functional? We answer this question when <span><math><mi>X</mi></math></span> is a random subset of a finite set. The result is then generalized to exponents which preserve complete monotonicity of functions on finite lattices. Also, we study the question of approximating an <span><math><mi>m</mi></math></span>-divisible random set by infinitely divisible random sets. We prove a theorem analogous to that of Arak’s classical result (Arak, 1981, 1982) on approximating an <span><math><mi>m</mi></math></span>-divisible random variable by infinitely divisible random variables.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104632"},"PeriodicalIF":1.1,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644464","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}