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We prove the the large deviation principle(LDP) for the law of the one-dimensional semilinear stochastic partial differential equations driven by nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation…

Probability · Mathematics 2023-03-09 Qiyong Cao , Hongjun Gao

This paper is concerned with the random effect of the noise dispersion for stochastic logarithmic Schr\"odinger equation emerged from the optical fibre with dispersion management. The well-posedness of the logarithmic Schr\"odinger equation…

Analysis of PDEs · Mathematics 2023-06-13 Jianbo Cui , Liying Sun

We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian…

Probability · Mathematics 2012-05-11 Parisa Fatheddin , Jie Xiong

We establish Freidlin-Wentzell results for a nonlinear ordinary differential equation starting close to the stable state $0$, say, subject to a perturbation by a stochastic integral which is driven by an $\varepsilon$-small and…

Probability · Mathematics 2020-06-22 André de Oliveira Gomes , Michael A. Högele

We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…

Probability · Mathematics 2024-08-13 Qiao Huang , Wei Wei , Jinqiao Duan

We prove the large deviations principle (LDP) for the law of the solutions to a class of semilinear stochastic partial differential equations driven by multiplicative noise. Our proof is based on the weak convergence approach and…

Probability · Mathematics 2016-07-05 Mohammud Foondun , Leila Setayeshgar

This paper considers the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with pure jump noise in Marcus canonical form, which describes the dynamics of magnetic spin field in a ferromagnet at elevated temperatures with the effective…

Analysis of PDEs · Mathematics 2024-08-13 Fan Xu , Bin Liu , Lei Zhang

We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0,1). It is also colored in space and the space correlation operator is assumed to be nuclear. We…

Probability · Mathematics 2007-11-08 Eric Gautier

We devise an explicit method to integrate $\alpha$-stable stochastic differential equations (SDEs) with non-Lipschitz coefficients. To mitigate against numerical instabilities caused by unbounded increments of the L\'evy noise, we use a…

Dynamical Systems · Mathematics 2021-06-04 Georg A. Gottwald , Ian Melbourne

This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by L\'evy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then,…

Probability · Mathematics 2025-01-28 Jiaohui Xu , Tomás Caraballo , José Valero

This work is devoted to non-linear stochastic Schr\"odinger equations with multiplicative fractional noise, where the stochastic integral is defined following the Riemann-Stieljes approach of Z\"ahle. Under the assumptions that the initial…

Analysis of PDEs · Mathematics 2013-04-01 Olivier Pinaud

We establish the large deviation principle for the slow variables in slow-fast dynamical system driven by both Brownian noises and L\'evy noises. The fast variables evolve at much faster time scale than the slow variables, but they are…

Dynamical Systems · Mathematics 2022-11-22 Shenglan Yuan , René Schilling , Jinqiao Duan

The aim of this article is to show the global existence of both martingale and pathwise solutions of stochastic equations with a monotone operator, of the Ladyzenskaya-Smagorinsky type, driven by a general Levy noise. The classical approach…

Analysis of PDEs · Mathematics 2021-04-27 Phuong Nguyen , Krutika Tawri , Roger Temam

In this paper, we establish the large deviation principles for stochastic porous media equations driven by time-dependent multiplicative noise on $\sigma$-finite measure space $(E,\mathcal{B}(E),\mu)$, and the Laplacian replaced by a…

Probability · Mathematics 2023-04-06 Weina Wu , Jianliang Zhai

In this article, we study the well-posedness theory for solutions of the stochastic heat equations with logarithmic nonlinearity perturbed by multiplicative Levy noise. By using Aldous tightness criteria and Jakubowski version of the…

Analysis of PDEs · Mathematics 2024-09-09 Kavin R , Ananta K Majee

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

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either…

chao-dyn · Physics 2008-02-03 P. Garbaczewski , J. R. Klauder , R. Olkiewicz

We study the small noise asymptotic for stochastic Burgers equations on $(0,1)$ with Dirichlet boundary condition. We consider the case that the noise is more singular than space-time white noise. We let the noise magnitude $\sqrt{\epsilon}…

Probability · Mathematics 2024-12-02 Rui Bai , Chunrong Feng , Huaizhong Zhao

In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which…

Probability · Mathematics 2015-05-20 Tarik El Mellali , Mohamed Mellouk

We study Freidlin-Wentzell's large deviation principle for one dimensional nonlinear stochastic heat equation driven by a Gaussian noise: $$\frac{\partial u^\varepsilon(t,x)}{\partial t} = \frac{\partial^2 u^\varepsilon(t,x)}{\partial…

Probability · Mathematics 2022-08-26 Ruinan Li , Ran Wang , Beibei Zhang