Stochastic Processes and their Applications最新文献

{"title":"Convergence rates for Chernoff-type approximations of convex monotone semigroups","authors":"Jonas Blessing ,&nbsp;Lianzi Jiang ,&nbsp;Michael Kupper ,&nbsp;Gechun Liang","doi":"10.1016/j.spa.2025.104700","DOIUrl":"10.1016/j.spa.2025.104700","url":null,"abstract":"<div><div>We provide explicit convergence rates for Chernoff-type approximations of convex monotone semigroups which have the form <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>f</mi><mo>=</mo><msub><mrow><mo>lim</mo></mrow><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></msub><mi>I</mi><msup><mrow><mrow><mo>(</mo><mfrac><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup><mi>f</mi></mrow></math></span> for bounded continuous functions <span><math><mi>f</mi></math></span>. Under suitable conditions on the one-step operators <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> regarding the time regularity and consistency of the approximation scheme, we obtain <span><math><mrow><msub><mrow><mo>‖</mo><mi>S</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>f</mi><mo>−</mo><mi>I</mi><msup><mrow><mrow><mo>(</mo><mfrac><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></mfrac><mo>)</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup><mi>f</mi><mo>‖</mo></mrow><mrow><mi>∞</mi></mrow></msub><mo>≤</mo><mi>c</mi><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mi>γ</mi></mrow></msup></mrow></math></span> for bounded Lipschitz continuous functions <span><math><mi>f</mi></math></span>, where <span><math><mrow><mi>c</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>γ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> are determined explicitly. Moreover, the mapping <span><math><mrow><mi>t</mi><mo>↦</mo><mi>S</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>f</mi></mrow></math></span> is Hölder continuous. These results are closely related to monotone approximation schemes for viscosity solutions but are obtained independently by following a recently developed semigroup approach to Hamilton–Jacobi–Bellman equations which uniquely characterizes semigroups via their <span><math><mi>Γ</mi></math></span>-generators. The different approach allows to consider convex rather than sublinear equations and the results can be extended to unbounded functions by modifying the norm with a suitable weight function. Furthermore, up to possibly different consistency errors for the operators <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, the upper and lower bound for the error between the semigroup and the iterated operators are symmetric. The abstract results are applied to Nisio semigroups and limit theorems for convex expectations.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104700"},"PeriodicalIF":1.1,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144288806","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":"Spectral bounds for exit times on metric measure Dirichlet spaces and applications","authors":"Phanuel Mariano ,&nbsp;Jing Wang","doi":"10.1016/j.spa.2025.104707","DOIUrl":"10.1016/j.spa.2025.104707","url":null,"abstract":"<div><div>Assuming the heat kernel on a doubling Dirichlet metric measure space has a sub-Gaussian bound, we prove an asymptotically sharp spectral upper bound on the survival probability of the associated diffusion process. As a consequence, we can show that the supremum of the mean exit time over all starting points is finite if and only if the bottom of the spectrum is positive. Among several applications, we show that the spectral upper bound on the survival probability implies a bound for the Hot Spots constant for Riemannian manifolds. Our results apply to interesting geometric settings including sub-Riemannian manifolds and fractals.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104707"},"PeriodicalIF":1.1,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322808","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":"Global central limit theorems for Markov chains","authors":"Christophe Cuny ,&nbsp;Michael Lin","doi":"10.1016/j.spa.2025.104709","DOIUrl":"10.1016/j.spa.2025.104709","url":null,"abstract":"<div><div>Let <span><math><mi>P</mi></math></span> be a Markov operator on a general state space <span><math><mrow><mo>(</mo><mi>S</mi><mo>,</mo><mi>Σ</mi><mo>)</mo></mrow></math></span> with invariant probability <span><math><mi>m</mi></math></span>, assumed ergodic. We study conditions which yield that for <em>every</em> centered <span><math><mrow><mn>0</mn><mo>≠</mo><mi>f</mi><mo>∈</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>m</mi><mo>)</mo></mrow></mrow></math></span> a non-degenerate annealed CLT and an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-normalized CLT hold.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"190 ","pages":"Article 104709"},"PeriodicalIF":1.1,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655378","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":"Discrete time optimal investment under model uncertainty","authors":"Laurence Carassus ,&nbsp;Massinissa Ferhoune","doi":"10.1016/j.spa.2025.104708","DOIUrl":"10.1016/j.spa.2025.104708","url":null,"abstract":"<div><div>We study a robust utility maximisation problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real line. She also faces model ambiguity in her beliefs about the market, which is modelled through a set of priors. We prove the existence of an optimal investment strategy using only primal methods. For that, we assume classical assumptions on the market and the random utility function as asymptotic elasticity constraints. Most of our other assumptions are stated on a prior-by-prior basis and correspond to generally accepted assumptions in the literature on markets without ambiguity. We also propose a general setting, including utility functions with benchmarks for which our assumptions can be easily checked.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"189 ","pages":"Article 104708"},"PeriodicalIF":1.1,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291409","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":"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":"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}