Stochastic Processes and their Applications最新文献

{"title":"Planar reinforced k-out percolation","authors":"Gideon Amir ,&nbsp;Markus Heydenreich ,&nbsp;Christian Hirsch","doi":"10.1016/j.spa.2025.104706","DOIUrl":"10.1016/j.spa.2025.104706","url":null,"abstract":"<div><div>We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses <span><math><mrow><mi>k</mi><mo>⩾</mo><mn>1</mn></mrow></math></span> incident edges, whose weight is then increased by 1. The choice of this <span><math><mi>k</mi></math></span>-tuple occurs proportionally to the product of the corresponding edge weights raised to some power <span><math><mrow><mi>α</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>.</div><div>Our investigations are guided by the conjecture that the set of infinitely reinforced edges percolates for <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>α</mi><mo>≫</mo><mn>1</mn></mrow></math></span>. First, we study the case <span><math><mrow><mi>α</mi><mo>=</mo><mi>∞</mi></mrow></math></span>, where we show the percolation for <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow></math></span> after adding arbitrarily sparse independent sprinkling and also allowing dual connectivities. We also derive a finite-size criterion for percolation without sprinkling. Then, we extend this finite-size criterion to the <span><math><mrow><mi>α</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span> case. Finally, we verify these conditions numerically.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104706"},"PeriodicalIF":1.1,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241427","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":"Percolation with random one-dimensional reinforcements","authors":"A. Nascimento ,&nbsp;R. Sanchis ,&nbsp;D. Ungaretti","doi":"10.1016/j.spa.2025.104704","DOIUrl":"10.1016/j.spa.2025.104704","url":null,"abstract":"<div><div>We study inhomogeneous Bernoulli bond percolation on the graph <span><math><mrow><mi>G</mi><mo>×</mo><mi>Z</mi></mrow></math></span>, where <span><math><mi>G</mi></math></span> is a connected quasi-transitive graph. The inhomogeneity is introduced through a random region <span><math><mi>R</mi></math></span> around the <em>origin axis</em> <span><math><mrow><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>×</mo><mi>Z</mi></mrow></math></span>, where each edge in <span><math><mi>R</mi></math></span> is open with probability <span><math><mi>q</mi></math></span> and all other edges are open with probability <span><math><mi>p</mi></math></span>. When the region <span><math><mi>R</mi></math></span> is defined by stacking or overlapping boxes with random radii centered along the origin axis, we derive conditions on the moments of the radii, based on the growth properties of <span><math><mi>G</mi></math></span>, so that for any subcritical <span><math><mi>p</mi></math></span> and any <span><math><mrow><mi>q</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the non-percolative phase persists.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104704"},"PeriodicalIF":1.1,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194425","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":"Sequential common change detection, isolation, and estimation in multiple compound Poisson processes","authors":"Dong-Yun Kim,&nbsp;Wei Biao Wu,&nbsp;Yanhong Wu","doi":"10.1016/j.spa.2025.104701","DOIUrl":"10.1016/j.spa.2025.104701","url":null,"abstract":"<div><div>We explore and compare the detection of changes in both the arrival rate and jump size mean and estimation of change-time after detection within a compound Poisson process by using generalized CUSUM and Shiryayev–Roberts (S–R) procedures. Average in-control and out-of control lengths are derived as well as the limiting distribution of the generalized CUSUM processes. The asymptotic bias of change time estimation is also derived. To detect a common change in multiple compound Poisson processes where change only occurs in a portion of panels, a unified algorithm is proposed that employs the sum of S–R processes to detect a common change, uses individual CUSUM processes to isolate the changed panels with False Discovery Rate (FDR) control, and then estimate the common change time as the median of the estimates obtained from the isolated channels. To illustrate the approach, we apply it to mining disaster data in the USA.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104701"},"PeriodicalIF":1.1,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144190340","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":"Majority dynamics on random graphs: The multiple states case","authors":"Jordan Chellig,&nbsp;Nikolaos Fountoulakis","doi":"10.1016/j.spa.2025.104682","DOIUrl":"10.1016/j.spa.2025.104682","url":null,"abstract":"<div><div>We study the evolution of majority dynamics with more than two states on the binomial random graph <span><math><mrow><mi>G</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>p</mi><mo>)</mo></mrow></mrow></math></span>. In this process, each vertex has a state in <span><math><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></mrow></math></span>, with <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, and at each round every vertex adopts state <span><math><mi>i</mi></math></span> if it has more neighbours in state <span><math><mi>i</mi></math></span> than in any other state. Ties are resolved randomly. We show that with high probability the process reaches unanimity in at most three rounds, if <span><math><mrow><mi>n</mi><mi>p</mi><mo>≫</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104682"},"PeriodicalIF":1.1,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203837","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":"Adapted Wasserstein distance between the laws of SDEs","authors":"Julio Backhoff-Veraguas ,&nbsp;Sigrid Källblad ,&nbsp;Benjamin A. Robinson","doi":"10.1016/j.spa.2025.104689","DOIUrl":"10.1016/j.spa.2025.104689","url":null,"abstract":"<div><div>We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals a novel connection between the synchronous coupling and the celebrated discrete-time Knothe–Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous-time processes. We complement our main results with examples showing how the optimal coupling may change in path-dependent and multidimensional settings.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104689"},"PeriodicalIF":1.1,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203836","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":"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":"On the multidimensional elephant random walk with stops","authors":"Bernard Bercu","doi":"10.1016/j.spa.2025.104692","DOIUrl":"10.1016/j.spa.2025.104692","url":null,"abstract":"<div><div>The goal of this paper is to investigate the asymptotic behavior of the multidimensional elephant random walk with stops (MERWS). In contrast with the standard elephant random walk, the elephant is allowed to stay on his own position. We prove that the Gram matrix associated with the MERWS, properly normalized, converges almost surely to the product of a deterministic matrix, related to the axes on which the MERWS moves uniformly, and a Mittag-Leffler distribution. It allows us to extend all the results previously established for the one-dimensional elephant random walk with stops. More precisely, in the diffusive and critical regimes, we prove the almost sure convergence of the MERWS. The asymptotic normality of the MERWS with a suitable random normalization is also provided. In the superdiffusive regime, we establish the almost sure convergence of the MERWS to a nondegenerate random vector. We also study the Gaussian fluctuations of the MERWS.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104692"},"PeriodicalIF":1.1,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144148049","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}