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This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…

Probability · Mathematics 2023-05-23 Bixiang Wang

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random…

Probability · Mathematics 2014-06-23 Damir Filipovic , Stefan Tappe , Josef Teichmann

We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, the process is…

Probability · Mathematics 2022-01-19 Daniel Adams , Gonçalo dos Reis , Romain Ravaille , William Salkeld , Julian Tugaut

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

Machine Learning · Statistics 2020-06-29 Martin Jørgensen , Marc Peter Deisenroth , Hugh Salimbeni

This paper is devoted to investigating Freidlin-Wentzell's large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation $\frac{\partial^2 u^{\e}(t,x)}{\partial t^2}=\frac{\partial^2 u^{\e}(t,x)}{\partial…

Probability · Mathematics 2022-11-29 Li Ruinan , Zhang Beibei

We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field, valid on balls of radius $R$, are…

Probability · Mathematics 2007-05-23 Shizan Fang , Peter Imkeller , Tusheng Zhang

In this article we prove new results regarding the existence and the uniqueness of global variational solutions to Neumann initial-boundary value problems for a class of non-autonomous stochastic parabolic partial differential equations.…

Analysis of PDEs · Mathematics 2018-06-29 Marco Dozzi , Rim Touibi , Pierre-A Vuillermot

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

We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…

Probability · Mathematics 2016-01-08 Luisa Beghin

These notes rigorously construct the stochastic integral of a Hilbert Space valued process driven by a Cylindrical Brownian Motion. We expand upon this stochastic calculus to present an introduction to stochastic differential equations in…

Probability · Mathematics 2023-09-15 Daniel Goodair

The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the convergence relies on a formal Hilbert expansion and the…

Analysis of PDEs · Mathematics 2014-05-13 Arnaud Debussche , Sylvain De Moor , Julien Vovelle

This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…

Dynamical Systems · Mathematics 2023-05-12 Bixiang Wang

A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…

Functional Analysis · Mathematics 2018-05-15 Alexei Daletskii

This paper establishes results on the existence and uniqueness of solutions to McKean-Vlasov equations, also called mean-field stochastic differential equations, in an infinite-dimensional Hilbert space setting with irregular drift. Here,…

Probability · Mathematics 2019-12-17 Martin Bauer , Thilo Meyer-Brandis

We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of…

Analysis of PDEs · Mathematics 2021-05-28 A. Es-Sarhir , M. Scheutzow , J. M. Tölle , O. van Gaans

In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic nonlinear Schr\"{o}dinger equation, with either focusing or defocusing nonlinearity, driven by nonlinear multiplicative L\'evy noise in the Marcus…

Probability · Mathematics 2024-08-19 Jiahui Zhu , Wei Liu , Jianliang Zhai

This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and…

Probability · Mathematics 2016-11-29 Erkan Nane , Yinan NI

The problem on identification of a limit of an ordinary differential equation with discontinuous drift that perturbed by a zero-noise is considered in multidimensional case. This problem is a classical subject of stochastic analysis.…

Probability · Mathematics 2015-10-06 Andrey Pilipenko , Frank Norbert Proske

This article is devoted to presenting an abstract theory on time-fractional gradient flows for nonconvex energy functionals in Hilbert spaces. Main results consist of local and global in time existence of (continuous) strong solutions to…

Analysis of PDEs · Mathematics 2025-01-15 Goro Akagi , Yoshihito Nakajima

Fractional (in time and in space) evolution equations defined on Dirichlet regular bounded open domains, driven by fractional integrated in time Gaussian spatiotemporal white noise, are considered here. Sufficient conditions for the…

Dynamical Systems · Mathematics 2017-01-17 V. V. Anh , N. N. Leonenko , M. D. Ruiz-Medina