Stochastic Processes and their Applications最新文献_第8页

Some remarks on the effect of the Random Batch Method on phase transition 关于随机分批法对相变影响的一些评论

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-10-16 DOI: 10.1016/j.spa.2024.104498

Arnaud Guillin , Pierre Le Bris , Pierre Monmarché

{"title":"Some remarks on the effect of the Random Batch Method on phase transition","authors":"Arnaud Guillin , Pierre Le Bris , Pierre Monmarché","doi":"10.1016/j.spa.2024.104498","DOIUrl":"10.1016/j.spa.2024.104498","url":null,"abstract":"<div><div>In this article, we focus on two toy models : the <em>Curie–Weiss</em> model and the system of <span><math><mi>N</mi></math></span> particles in linear interactions in a <em>double well confining potential</em>. Both models, which have been extensively studied, describe a large system of particles with a mean-field limit that admits a phase transition. We are concerned with the numerical simulation of these particle systems. To deal with the quadratic complexity of the numerical scheme, corresponding to the computation of the <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> interactions per time step, the <em>Random Batch Method</em> (RBM) has been suggested. It consists in randomly (and uniformly) dividing the particles into batches of size <span><math><mrow><mi>p</mi><mo>></mo><mn>1</mn></mrow></math></span>, and computing the interactions only within each batch, thus reducing the numerical complexity to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>N</mi><mi>p</mi><mo>)</mo></mrow></mrow></math></span> per time step. The convergence of this numerical method has been proved in other works.</div><div>This work is motivated by the observation that the RBM, via the random constructions of batches, artificially adds noise to the particle system. The goal of this article is to study the effect of this added noise on the phase transition of the nonlinear limit, and more precisely we study the <em>effective dynamics</em> of the two models to show how a phase transition may still be observed with the RBM but at a lower critical temperature.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"179 ","pages":"Article 104498"},"PeriodicalIF":1.1,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532078","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}

引用次数: 0

Stochastic representation for solutions of a system of coupled HJB-Isaacs equations with integral–differential operators 带积分微分算子的 HJB-Isaacs 耦合方程组解的随机表示法

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-10-15 DOI: 10.1016/j.spa.2024.104502

Sheng Luo , Wenqiang Li , Xun Li , Qingmeng Wei

{"title":"Stochastic representation for solutions of a system of coupled HJB-Isaacs equations with integral–differential operators","authors":"Sheng Luo , Wenqiang Li , Xun Li , Qingmeng Wei","doi":"10.1016/j.spa.2024.104502","DOIUrl":"10.1016/j.spa.2024.104502","url":null,"abstract":"<div><div>In this paper, we focus on the stochastic representation of a system of coupled Hamilton–Jacobi–Bellman–Isaacs (HJB–Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs’ type integral-partial differential equation. For this, we introduce an associated zero-sum stochastic differential game, where the state process is described by a classical stochastic differential equation (SDE, for short) with jumps, and the cost functional of recursive type is defined by a new type of backward stochastic differential equation (BSDE, for short) with two Poisson random measures, whose wellposedness and a prior estimate as well as the comparison theorem are investigated for the first time. One of the Poisson random measures <span><math><mi>μ</mi></math></span> appearing in the SDE and the BSDE stems from the integral term of the HJBI equations; the other random measure in BSDE is introduced to link the coupling factor of the HJBI equations. We show through an extension of the dynamic programming principle that the lower value function of this game problem is the viscosity solution of the system of our coupled HJBI equations. The uniqueness of the viscosity solution is also obtained in a space of continuous functions satisfying certain growth condition. In addition, also the upper value function of the game is shown to be the solution of the associated system of coupled Isaacs’ type of integral-partial differential equations. As a byproduct, we obtain the existence of the value for the game problem under the well-known Isaacs’ condition.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"179 ","pages":"Article 104502"},"PeriodicalIF":1.1,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532073","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}

引用次数: 0

Mixed orthogonality graphs for continuous-time stationary processes 连续时间静止过程的混合正交图

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-10-09 DOI: 10.1016/j.spa.2024.104501

Vicky Fasen-Hartmann, Lea Schenk

{"title":"Mixed orthogonality graphs for continuous-time stationary processes","authors":"Vicky Fasen-Hartmann, Lea Schenk","doi":"10.1016/j.spa.2024.104501","DOIUrl":"10.1016/j.spa.2024.104501","url":null,"abstract":"<div><div>In this paper, we introduce different concepts of Granger causality and contemporaneous correlation for multivariate stationary continuous-time processes to model different dependencies between the component processes. Several equivalent characterisations are given for the different definitions, in particular by orthogonal projections. We then define two mixed graphs based on different definitions of Granger causality and contemporaneous correlation, the (mixed) orthogonality graph and the local (mixed) orthogonality graph. In these graphs, the components of the process are represented by vertices, directed edges between the vertices visualise Granger causal influences and undirected edges visualise contemporaneous correlation between the component processes. Further, we introduce various notions of Markov properties in analogy to Eichler (2012), which relate paths in the graphs to different dependence structures of subprocesses, and we derive sufficient criteria for the (local) orthogonality graph to satisfy them. Finally, as an example, for the popular multivariate continuous-time AR (MCAR) processes, we explicitly characterise the edges in the (local) orthogonality graph by the model parameters.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"179 ","pages":"Article 104501"},"PeriodicalIF":1.1,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532081","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}

引用次数: 0

On weak and strong solutions of time inhomogeneous Itô’s equations with VMO diffusion and Morrey drift 关于具有 VMO 扩散和莫雷漂移的时间不均匀伊托方程的弱解和强解

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-10-09 DOI: 10.1016/j.spa.2024.104505

N.V. Krylov

引用次数: 0

Well-Posedness of the generalised Dean–Kawasaki Equation with correlated noise on bounded domains 有界域上具有相关噪声的广义迪安-川崎方程的良好拟合性

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-10-09 DOI: 10.1016/j.spa.2024.104503

Shyam Popat

引用次数: 0

Dual process in the two-parameter Poisson–Dirichlet diffusion 双参数泊松-狄利克特扩散中的双重过程

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-10-05 DOI: 10.1016/j.spa.2024.104500

Robert C. Griffiths , Matteo Ruggiero , Dario Spanò , Youzhou Zhou

{"title":"Dual process in the two-parameter Poisson–Dirichlet diffusion","authors":"Robert C. Griffiths , Matteo Ruggiero , Dario Spanò , Youzhou Zhou","doi":"10.1016/j.spa.2024.104500","DOIUrl":"10.1016/j.spa.2024.104500","url":null,"abstract":"<div><div>The two-parameter Poisson–Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson–Dirichlet stationary distribution. Here we identify a dual process for this diffusion and obtain its transition probabilities. The dual is shown to be given by Kingman’s coalescent with mutation, conditional on a given configuration of leaves. Interestingly, the dual depends on the additional parameter of the stationary distribution only through the test functions and not through the transition rates. After discussing the sampling probabilities of a two-parameter Poisson–Dirichlet partition drawn conditionally on another partition, we use these notions together with the dual process to derive the transition density of the diffusion. Our derivation provides a new probabilistic proof of this result, leveraging on an extension of Pitman’s Pólya urn scheme, whereby the urn is split after a finite number of steps and two urns are run independently onwards. The proof strategy exemplifies the power of duality and could be exported to other models where a dual is available.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"179 ","pages":"Article 104500"},"PeriodicalIF":1.1,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420923","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}

引用次数: 0

Erratum to: “Statistical test for an urn model with random multidrawing and random addition” [Stochastic Process. Appl. 158 (2023) 342-360] 勘误："随机多抽签和随机添加的瓮模型统计检验》[《随机过程。应用》158 (2023) 342-360] 更正

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-10-05 DOI: 10.1016/j.spa.2024.104495

Irene Crimaldi , Pierre-Yves Louis , Ida G. Minelli

引用次数: 0

Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes 罗森布拉特过程驱动的 SDE 的参数估计和路径空间上的奇异规律

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-10-05 DOI: 10.1016/j.spa.2024.104499

Petr Čoupek, Pavel Kříž, Bohdan Maslowski

引用次数: 0

Weak convergence of continuous-state branching processes with large immigration 大量移民的连续状态分支过程的弱收敛性

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-09-30 DOI: 10.1016/j.spa.2024.104497

Clément Foucart , Linglong Yuan

引用次数: 0

Geodesics cross any pattern in first-passage percolation without any moment assumption and with possibly infinite passage times 测地线在第一通道渗流中穿过任何模式，无需任何矩假设，且通道时间可能无限长

IF 1.1 2区数学

Stochastic Processes and their Applications Pub Date : 2024-09-27 DOI: 10.1016/j.spa.2024.104496

Antonin Jacquet

{"title":"Geodesics cross any pattern in first-passage percolation without any moment assumption and with possibly infinite passage times","authors":"Antonin Jacquet","doi":"10.1016/j.spa.2024.104496","DOIUrl":"10.1016/j.spa.2024.104496","url":null,"abstract":"<div><div>In first-passage percolation, one places nonnegative i.i.d. random variables (<span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></mrow></math></span>) on the edges of <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. A geodesic is an optimal path for the passage times <span><math><mrow><mi>T</mi><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></mrow></math></span>. Consider a local property of the time environment. We call it a pattern. We investigate the number of times a geodesic crosses a translate of this pattern. When we assume that the common distribution of the passage times satisfies a suitable moment assumption, it is shown in [Antonin Jacquet. Geodesics in first-passage percolation cross any pattern, arXiv:2204.02021, 2023] that, apart from an event with exponentially small probability, this number is linear in the distance between the extremities of the geodesic. This paper completes this study by showing that this result remains true when we consider distributions with an unbounded support without any moment assumption or distributions with possibly infinite passage times. The techniques of proof differ from the preceding article and rely on a notion of penalized geodesic.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"179 ","pages":"Article 104496"},"PeriodicalIF":1.1,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421383","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}

引用次数: 0