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This paper establishes a Freidlin-Wentzell large deviation principle for stochastic differential equations(SDEs) under locally weak monotonicity conditions and Lyapunov conditions. We illustrate the main result of the paper by showing that…

Probability · Mathematics 2021-10-14 Jian Wang , Hao Yang , Jianliang Zhai , Tusheng Zhang

In this paper, we first establish well-posedness results for one-dimensional McKean-Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial…

Probability · Mathematics 2024-03-29 Gunther Leobacher , Christoph Reisinger , Wolfgang Stockinger

The purpose of this paper is to establish asymptotic behaviors of time-inhomogeneous multi-scale stochastic differential equations (SDEs). To achieve them, we analyze the evolution system of measures for time-inhomogeneous Markov…

Probability · Mathematics 2024-12-16 Xiaobin Sun , Jian Wang , Yingchao Xie

In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular $L^p$-interactions as well as for the moderate interaction particle systems on the level of particle…

Probability · Mathematics 2022-06-17 Zimo Hao , Michael Röckner , Xicheng Zhang

In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…

Probability · Mathematics 2025-09-30 Jie Xiang , Huijie Qiao

We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump L\'{e}vy processes. We prove a uniform in time propagation of chaos result, providing quantitative bounds on…

Probability · Mathematics 2020-11-10 Mingjie Liang , Mateusz B. Majka , Jian Wang

Building on the well-posedness of the backward Kolmogorov partial differential equation in the Wasserstein space, we analyze the strong and weak convergence rates for approximating the unique solution of a class of McKean-Vlasov stochastic…

Probability · Mathematics 2025-03-31 Noufel Frikha , Xuanye Song

In this paper, we study the asymptotic behavior of randomly perturbed path-dependent stochastic differential equations with small parameter $\vartheta_{\varepsilon}$, when $\varepsilon \rightarrow 0$, $\vartheta_\varepsilon$ goes to $0$.…

Probability · Mathematics 2023-04-03 Liu Xiangdong , Hong Shaopeng

We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with It\^o noise for particle systems with mean-field interactions both on the drift and the noise. The global existence and uniqueness of the…

Probability · Mathematics 2025-03-03 Ana Djurdjevac , Xiaohao Ji , Nicolas Perkowski

This paper is devoted to investigating the Freidlin-Wentzell's large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak…

Probability · Mathematics 2021-06-29 Wei Hong , Shihu Li , Wei Liu

In this paper, we establish the weak averaging principle for stochastic functional partial differential equations (in short, SFPDEs) with H$\ddot{\text{o}}$lder continuous coefficients and infinite delay by a new generalized coupling…

Probability · Mathematics 2025-03-31 Shuaishuai Lu , Xue Yang , Yong Li

In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…

Probability · Mathematics 2020-07-02 Jasper Hoeksema , Thomas Holding , Mario Maurelli , Oliver Tse

In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…

Analysis of PDEs · Mathematics 2018-10-03 Manh Hong Duong , Julian Tugaut

This paper studies McKean-Vlasov stochastic differential equations (MVSDEs) whose drift coefficients grow super-linearly in both state variables and measure arguments, and whose diffusion coefficients exhibit super-linear growth in the…

Probability · Mathematics 2026-02-09 Zhuoqi Liu , Qian Guo , Shuaibin Gao , Chenggui Yuan

We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…

Numerical Analysis · Mathematics 2025-02-10 Jiamin Jian , Qingshuo Song , Xiaojie Wang , Zhongqiang Zhang , Yuying Zhao

We utilize the weak convergence method to establish the Freidlin--Wentzell large deviations principle (LDP) for stochastic delay differential equations (SDDEs) with super-linearly growing coefficients, which covers a large class of cases…

Probability · Mathematics 2022-01-04 Diancong Jin , Ziheng Chen , Tau Zhou

We present a comprehensive discretization scheme for linear and nonlinear stochastic differential equations (SDEs) driven by either Brownian motions or $\alpha$-stable processes. Our approach utilizes compound Poisson particle…

Probability · Mathematics 2023-07-14 Xicheng Zhang

In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong…

Numerical Analysis · Mathematics 2025-10-21 Jingtao Zhu , Yuying Zhao , Siqing Gan

As an important tool characterizing the long time behavior of Markov processes, the Donsker-Varadhan LDP (large deviation principle) does not directly apply to distribution dependent SDEs/SPDEs since the solutions are non-Markovian. We…

Probability · Mathematics 2020-02-21 Panpan Ren , Feng-Yu Wang

Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…

Probability · Mathematics 2015-10-09 Amarjit Budhiraja , Ruoyu Wu