Stochastic Processes and their Applications最新文献

{"title":"Smoothness estimation for Whittle–Matérn processes on closed Riemannian manifolds","authors":"Moritz Korte-Stapff ,&nbsp;Toni Karvonen ,&nbsp;Éric Moulines","doi":"10.1016/j.spa.2025.104685","DOIUrl":"10.1016/j.spa.2025.104685","url":null,"abstract":"<div><div>The family of Matérn kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for example, optimal error bounds for kriging and posterior contraction rates in Gaussian process regression. On closed Riemannian manifolds, we show that the smoothness parameter can be consistently estimated from the maximizer(s) of the Gaussian likelihood when the underlying data are from point evaluations of a Gaussian process and, perhaps surprisingly, even when the data comprise evaluations of a non-Gaussian process. The points at which the process is observed need not have any particular spatial structure beyond quasi-uniformity. Our methods are based on results from approximation theory for the Sobolev scale of Hilbert spaces. Moreover, we generalize a well-known equivalence of measures phenomenon related to Matérn kernels to the non-Gaussian case by using Kakutani’s theorem.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104685"},"PeriodicalIF":1.1,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203824","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":"Strong regularization by noise for a class of kinetic SDEs driven by symmetric α-stable processes","authors":"Giacomo Lucertini ,&nbsp;Stéphane Menozzi ,&nbsp;Stefano Pagliarani","doi":"10.1016/j.spa.2025.104691","DOIUrl":"10.1016/j.spa.2025.104691","url":null,"abstract":"<div><div>We establish strong well-posedness for a class of degenerate SDEs of kinetic type with autonomous diffusion driven by a symmetric <span><math><mi>α</mi></math></span>-stable process under Hölder regularity conditions for the drift term. We partially recover the thresholds for the Hölder regularity that are optimal for weak uniqueness. In general dimension, we only consider <span><math><mrow><mi>α</mi><mo>=</mo><mn>2</mn></mrow></math></span> and need an additional integrability assumption for the gradient of the drift: this condition is satisfied by Peano-type functions. In the one-dimensional case we do not need any additional assumption. In the multi-dimensional case, the proof is based on a first-order Zvonkin transform/PDE, while for the one-dimensional case we use a second-order Zvonkin/PDE transform together with a Watanabe–Yamada technique.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104691"},"PeriodicalIF":1.1,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144148048","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":"On the particle approximation of lagged Feynman–Kac formulae","authors":"Elsiddig Awadelkarim ,&nbsp;Michel Caffarel ,&nbsp;Pierre Del Moral ,&nbsp;Ajay Jasra","doi":"10.1016/j.spa.2025.104690","DOIUrl":"10.1016/j.spa.2025.104690","url":null,"abstract":"<div><div>In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman–Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function. The typical application considered here is the computation of eigenvalues associated with non-negative operators as found, for example, in physics or particle simulation of rare-events. We focus on a novel <em>lagged</em> approximation of this invariant measure, based upon the introduction of a ratio of time-averaged Feynman–Kac marginals associated with a positive operator iterated <span><math><mrow><mi>l</mi><mo>∈</mo><mi>N</mi></mrow></math></span> times; a lagged Feynman–Kac formula. This estimator and its approximation using Diffusion Monte Carlo (DMC) are commonly used in the physics literature. In short, DMC is an iterative algorithm involving <span><math><mrow><mi>N</mi><mo>∈</mo><mi>N</mi></mrow></math></span> particles or walkers simulated in parallel, that undergo sampling and resampling operations. In this work, it is shown that for the DMC approximation of the lagged Feynman–Kac formula, one has an almost sure characterization of the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-error as the time parameter (iteration) goes to infinity and this is at most of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mo>exp</mo><mrow><mo>{</mo><mo>−</mo><mi>κ</mi><mi>l</mi><mo>}</mo></mrow><mo>/</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span>, for <span><math><mrow><mi>κ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. In addition a non-asymptotic in time, and time uniform <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo></mrow></math></span>bound is proved which is <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>l</mi><mo>/</mo><msqrt><mrow><mi>N</mi></mrow></msqrt><mo>)</mo></mrow></mrow></math></span>. We also prove a novel central limit theorem to give a characterization of the exact asymptotic in time variance. This analysis demonstrates that the strategy used in physics, namely, to run DMC with <span><math><mi>N</mi></math></span> and <span><math><mi>l</mi></math></span> small and, for long time enough, is mathematically justified. Our results also suggest how one should choose <span><math><mi>N</mi></math></span> and <span><math><mi>l</mi></math></span> in practice. We emphasize that these results are not restricted to physical applications; they have broad relevance to the general problem of particle simulation of the Feynman–Kac formula, which is utilized in a great variety of scientific and engineering fields.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104690"},"PeriodicalIF":1.1,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116899","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":"Risk-sensitive continuous-time stochastic games with the average criterion and a compact state space","authors":"Xin Guo,&nbsp;Zewu Zheng","doi":"10.1016/j.spa.2025.104688","DOIUrl":"10.1016/j.spa.2025.104688","url":null,"abstract":"<div><div>This paper attempts to study <em>the risk-sensitive average continuous-time stochastic game</em> with compact state and action spaces. We derive an equivalent Shapley equation for the risk-sensitive average criterion. By building a novel parametric operator and analyzing the properties of an eigenvalue of the operator, we prove the equivalent Shapley equation admits a solution, and then establish the existence of the value and a Nash equilibrium over the class of history-dependent policies. Moreover, we design an iterative algorithm for computing the value of the game and prove the convergence of the algorithm. Finally, two examples are given to verify our results.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104688"},"PeriodicalIF":1.1,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106650","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":"On the limit theory of mean field optimal stopping with non-Markov dynamics and common noise","authors":"Xihao He","doi":"10.1016/j.spa.2025.104681","DOIUrl":"10.1016/j.spa.2025.104681","url":null,"abstract":"<div><div>This paper focuses on a mean-field optimal stopping problem with non-Markov dynamics and common noise, inspired by Talbi et al. (2025,2022). The goal is to establish the limit theory and demonstrate the equivalence of the value functions between weak and strong formulations. The difference between the strong and weak formulations lies in the source of randomness determining the stopping time on a canonical space. In the strong formulation, the randomness of the stopping time originates from Brownian motions. In contrast, this may not necessarily be the case in the weak formulation. Additionally, a <span><math><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></math></span>-Hypothesis-type condition is introduced to guarantee the equivalence of the value functions. The limit theory encompasses the convergence of the value functions and solutions of the large population optimal stopping problem towards those of the mean-field limit, and it shows that every solution of the mean field optimal stopping problem can be approximated by solutions of the large population optimal stopping problem.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104681"},"PeriodicalIF":1.1,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106651","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":"Taming under isoperimetry","authors":"Iosif Lytras ,&nbsp;Sotirios Sabanis","doi":"10.1016/j.spa.2025.104684","DOIUrl":"10.1016/j.spa.2025.104684","url":null,"abstract":"<div><div>In this article we propose a novel taming Langevin-based scheme called <span><math><mi>sTULA</mi></math></span> to sample from distributions with superlinearly growing log-gradient which also satisfy a Log-Sobolev inequality. We derive non-asymptotic convergence bounds in <span><math><mrow><mi>K</mi><mi>L</mi></mrow></math></span> and consequently total variation and Wasserstein-2 distance from the target measure. Non-asymptotic convergence guarantees are provided for the performance of the new algorithm as an optimizer. Finally, some theoretical results on isoperimertic inequalities for distributions with superlinearly growing gradients are provided. Key findings are a Log-Sobolev inequality with constant independent of the dimension, in the presence of a higher order regularization and a Poincaré inequality with constant independent of temperature and dimension under a novel non-convex theoretical framework.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104684"},"PeriodicalIF":1.1,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950503","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":"Quantitative hydrodynamics for a generalized contact model","authors":"Julian Amorim,&nbsp;Milton Jara,&nbsp;Yangrui Xiang","doi":"10.1016/j.spa.2025.104680","DOIUrl":"10.1016/j.spa.2025.104680","url":null,"abstract":"<div><div>We derive a quantitative version of the hydrodynamic limit obtained in Chariker et al. (2023) for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-speed of convergence of the empirical density of states in a generalized contact process defined over a <span><math><mi>d</mi></math></span>-dimensional torus of size <span><math><mi>n</mi></math></span> is of the optimal order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>d</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>. In addition, we show that the typical fluctuations around the aforementioned hydrodynamic limit are Gaussian, and governed by an inhomogeneous stochastic linear equation.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104680"},"PeriodicalIF":1.1,"publicationDate":"2025-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950504","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":"Some quenched and annealed limit theorems for superprocesses in random environments","authors":"Zeteng Fan,&nbsp;Jieliang Hong ,&nbsp;Jie Xiong","doi":"10.1016/j.spa.2025.104686","DOIUrl":"10.1016/j.spa.2025.104686","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>X</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span> be a superprocess in a random environment described by a Gaussian noise <span><math><mrow><mi>W</mi><mo>=</mo><mrow><mo>{</mo><mi>W</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>}</mo></mrow></mrow></math></span> white in time and colored in space with correlation kernel <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span>. When <span><math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, under the condition that the correlation function <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span> is bounded above by some appropriate function <span><math><mrow><mover><mrow><mi>g</mi></mrow><mrow><mo>̄</mo></mrow></mover><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span>, we present the quenched and annealed Strong Law of Large Numbers and the Central Limit Theorems regarding the weighted occupation measure <span><math><mrow><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mi>t</mi></mrow></msubsup><msub><mrow><mi>X</mi></mrow><mrow><mi>s</mi></mrow></msub><mi>d</mi><mi>s</mi></mrow></math></span> as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104686"},"PeriodicalIF":1.1,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950502","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":"Averaging principle for semilinear slow–fast rough partial differential equations","authors":"Miaomiao Li ,&nbsp;Yunzhang Li ,&nbsp;Bin Pei ,&nbsp;Yong Xu","doi":"10.1016/j.spa.2025.104683","DOIUrl":"10.1016/j.spa.2025.104683","url":null,"abstract":"<div><div>In this paper, we investigate the averaging principle for a class of semilinear slow–fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random <span><math><mi>γ</mi></math></span>-Hölder rough path for some <span><math><mrow><mi>γ</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, while the fast component is driven by an Itô-type Brownian rough path. Using controlled rough path theory and the classical Khasminskii’s time discretization scheme, we demonstrate that the slow component converges strongly to the solution of the corresponding averaged equation under the Hölder topology.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104683"},"PeriodicalIF":1.1,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084498","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":"Stationary entrance chains and applications to random walks","authors":"Aleksandar Mijatović ,&nbsp;Vladislav Vysotsky","doi":"10.1016/j.spa.2025.104668","DOIUrl":"10.1016/j.spa.2025.104668","url":null,"abstract":"<div><div>For a Markov chain <span><math><mi>Y</mi></math></span> with values in a Polish space, consider the <em>entrance chain</em> obtained by sampling <span><math><mi>Y</mi></math></span> at the moments when it enters a fixed set <span><math><mi>A</mi></math></span> from its complement <span><math><msup><mrow><mi>A</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span>. Similarly, consider the <em>exit chain</em>, obtained by sampling <span><math><mi>Y</mi></math></span> at the exit times from <span><math><msup><mrow><mi>A</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span> to <span><math><mi>A</mi></math></span>. We use the method of inducing from ergodic theory to study invariant measures of these two types of Markov chains in the case when the initial chain <span><math><mi>Y</mi></math></span> has a known invariant measure. We give explicit formulas for invariant measures of the entrance and exit chains under certain recurrence-type assumptions on <span><math><mi>A</mi></math></span> and <span><math><msup><mrow><mi>A</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span>, which apply even for transient chains. Then we study uniqueness and ergodicity of these invariant measures assuming that <span><math><mi>Y</mi></math></span> is topologically recurrent, topologically irreducible, and weak Feller.</div><div>We give applications to random walks in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, which we regard as “stationary” Markov chains started under the Lebesgue measure. We are mostly interested in dimension one, where we study the Markov chain of overshoots above the zero level of a random walk that oscillates between <span><math><mrow><mo>−</mo><mi>∞</mi></mrow></math></span> and <span><math><mrow><mo>+</mo><mi>∞</mi></mrow></math></span>. We show that this chain is ergodic, and use this result to prove a central limit theorem for the number of level crossings of a random walk with zero mean and finite variance of increments.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"188 ","pages":"Article 104668"},"PeriodicalIF":1.1,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942254","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}