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A Palm space approach to non-linear Hawkes processes 非线性霍克斯过程的帕姆空间方法
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2024-01-01 DOI: 10.1214/23-ejp1063
Philippe Robert, Gaetan Vignoud
{"title":"A Palm space approach to non-linear Hawkes processes","authors":"Philippe Robert, Gaetan Vignoud","doi":"10.1214/23-ejp1063","DOIUrl":"https://doi.org/10.1214/23-ejp1063","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"37 10","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139456710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 evolution equations with Wick-polynomial nonlinearities 具有wick -多项式非线性的随机演化方程
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-03-10 DOI: 10.1214/18-EJP241
T. Levajković, S. Pilipovic, D. Seleši, M. Zigic
{"title":"Stochastic evolution equations with Wick-polynomial nonlinearities","authors":"T. Levajković, S. Pilipovic, D. Seleši, M. Zigic","doi":"10.1214/18-EJP241","DOIUrl":"https://doi.org/10.1214/18-EJP241","url":null,"abstract":"We study nonlinear parabolic stochastic partial differential equations with Wick-power and Wick-polynomial type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fujita equation, the stochastic Fisher-KPP equation and the stochastic FitzHugh-Nagumo equation among many others. By implementing the theory of $C_0-$semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove existence and uniqueness of solutions for this class of SPDEs. In particular, we also treat the linear nonautonomous case and provide several applications featured as stochastic reaction-diffusion equations that arise in biology, medicine and physics.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"23 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48741498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
A composite generalization of Ville’s martingale theorem using e-processes 用e过程对维尔鞅定理的复合推广
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1019
Johannes Ruf, Martin Larsson, Wouter M. Koolen, Aaditya Ramdas
{"title":"A composite generalization of Ville’s martingale theorem using e-processes","authors":"Johannes Ruf, Martin Larsson, Wouter M. Koolen, Aaditya Ramdas","doi":"10.1214/23-ejp1019","DOIUrl":"https://doi.org/10.1214/23-ejp1019","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135213398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Wasserstein contraction and spectral gap of slice sampling revisited 重新讨论了切片采样的Wasserstein收缩和谱隙
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1030
Philip Schär
{"title":"Wasserstein contraction and spectral gap of slice sampling revisited","authors":"Philip Schär","doi":"10.1214/23-ejp1030","DOIUrl":"https://doi.org/10.1214/23-ejp1030","url":null,"abstract":"We propose a new class of Markov chain Monte Carlo methods, called k-polar slice sampling (k-PSS), as a technical tool that interpolates between and extrapolates beyond uniform and polar slice sampling. By examining Wasserstein contraction rates and spectral gaps of k-PSS, we obtain strong quantitative results regarding its performance for different kinds of target distributions. Because k-PSS contains uniform and polar slice sampling as special cases, our results significantly advance the theoretical understanding of both of these methods. In particular, we prove realistic estimates of the convergence rates of uniform slice sampling for arbitrary multivariate Gaussian distributions on the one hand, and near-arbitrary multivariate t-distributions on the other. Furthermore, our results suggest that for heavy-tailed distributions, polar slice sampling performs dimension-independently well, whereas uniform slice sampling suffers a rather strong curse of dimensionality.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"276 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
Contact process in an evolving random environment 随机环境下的接触过程
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1002
Marco Seiler, Anja Sturm
{"title":"Contact process in an evolving random environment","authors":"Marco Seiler, Anja Sturm","doi":"10.1214/23-ejp1002","DOIUrl":"https://doi.org/10.1214/23-ejp1002","url":null,"abstract":"In this paper we introduce a contact process in an evolving random environment (CPERE) on a connected and transitive graph with bounded degree, where we assume that this environment is described through an ergodic spin systems with finite range. We show that under a certain growth condition the phase transition of survival is independent of the initial configuration of the process. We study the invariant laws of the CPERE and show that under aforementioned growth condition the phase transition for survival coincides with the phase transition of non-triviality of the upper invariant law. Furthermore, we prove continuity properties for the survival probability and derive equivalent conditions for complete convergence, in an analogous way as for the classical contact process. We then focus on the special case, where the evolving random environment is described through a dynamical percolation. We show that the contact process on a dynamical percolation on the d-dimensional integers dies out almost surely at criticality and complete convergence holds for all parameter choices. In the end we derive some comparison results between a dynamical percolation and ergodic spin systems with finite range such that we get bounds on the survival probability of a contact process in an evolving random environment and we determine in this case that complete convergence holds in a certain parameter regime.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
Simple random walk on Z2 perturbed on the axes (renewal case) 在坐标轴上扰动的Z2上的简单随机游走(更新情况)
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp969
Pierre Andreoletti, P. Debs
{"title":"Simple random walk on Z2 perturbed on the axes (renewal case)","authors":"Pierre Andreoletti, P. Debs","doi":"10.1214/23-ejp969","DOIUrl":"https://doi.org/10.1214/23-ejp969","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48018140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Sharp estimates for martingale transforms with unbounded transforming sequences 具有无界变换序列的鞅变换的Sharp估计
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp953
T. Gałązka, A. Osȩkowski
{"title":"Sharp estimates for martingale transforms with unbounded transforming sequences","authors":"T. Gałązka, A. Osȩkowski","doi":"10.1214/23-ejp953","DOIUrl":"https://doi.org/10.1214/23-ejp953","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49192598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Lévy flows and associated stochastic PDEs 柳青流动和相关的随机偏微分方程
IF 1.4 3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp959
Arvind Nath, Suprio Bhar
{"title":"Lévy flows and associated stochastic PDEs","authors":"Arvind Nath, Suprio Bhar","doi":"10.1214/23-ejp959","DOIUrl":"https://doi.org/10.1214/23-ejp959","url":null,"abstract":"","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42724960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 1
A micro-macro variational formula for the free energy of a many-body system with unbounded marks 具有无界标记的多体系统自由能的微观-宏观变分公式
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp1014
Orphée Collin, Benedikt Jahnel, Wolfgang König
{"title":"A micro-macro variational formula for the free energy of a many-body system with unbounded marks","authors":"Orphée Collin, Benedikt Jahnel, Wolfgang König","doi":"10.1214/23-ejp1014","DOIUrl":"https://doi.org/10.1214/23-ejp1014","url":null,"abstract":"The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the famous Bose–Einstein condensation phase transition is sought for. A qualitative understanding of the free energy would be helpful, but this is currently far out of reach. In this paper, we demonstrate a path towards gaining such an understanding for a simplified version of the model with deterministic boxes instead of Brownian cycles. This model is a marked Poisson point process with unbounded marks containing particles and bounded-reach interactions between the particles. Even though it is not a quantum model, it is close to that in spirit. We derive an explicit and interpretable variational formula in the thermodynamic limit for the limiting free energy of the canonical ensemble for any value of the particle density. This formula features all relevant physical quantities of the model, like the microscopic and the macroscopic particle densities, together with their mutual and self-energies and their entropies. The proof method comprises a two-step meso-macro large-deviation approach for marked Poisson point processes and an explicit distinction into small and large marks; an application of well-known level-three principles á la Georgii/Zessin is not possible because of the appearance of macro marks. The characteristic variational formula enables us to prove a number of properties of the limiting free energy as a function of the particle density, like differentiability and explicit upper and lower bounds, and a qualitative picture below and above the critical threshold (if it is finite). This proves a modified saturation nature of the phase transition. However, we have not yet succeeded in proving the existence of this phase transition.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135212403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Dynamic programming approach to reflected backward stochastic differential equations 反映后向随机微分方程的动态规划方法
3区 数学
Electronic Journal of Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ejp999
Hun O, Mun-Chol Kim, Kon-Gun Kim
{"title":"Dynamic programming approach to reflected backward stochastic differential equations","authors":"Hun O, Mun-Chol Kim, Kon-Gun Kim","doi":"10.1214/23-ejp999","DOIUrl":"https://doi.org/10.1214/23-ejp999","url":null,"abstract":"By introducing a new type of minimality condition, this paper gives a novel approach to the reflected backward stochastic differential equations (RBSDEs) with càdlàg obstacles. Our first step is to prove the dynamic programming principles for nonlinear optimal stopping problems with g-expectations. We then use the nonlinear Doob-Meyer decomposition theorem for g-supermartingales to get the existence of the solution. With a new type of minimality condition, we prove a representation formula of solutions to RBSDEs, in an efficient way. Finally, we derive some a priori estimates and stability results.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136008514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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