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In this paper, we are concerned with multi-scale distribution dependent stochastic differential equations driven by fractional Brownian motion (with Hurst index $H>\frac12$ and standard Brownian motion, simultaneously. Our aim is to…

Probability · Mathematics 2023-06-12 Shen Gunagjun , Zhou Huan , Wu Jianglun

In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.

Probability · Mathematics 2016-11-01 Yumeng Li , Ran Wang , Nian Yao , Shuguang Zhang

In this paper, we prove the large deviation principle (LDP) for stochastic differential equations driven by stochastic integrals in one dimension. The result can be proved with a minimal use of rough path theory, and this implies the LDP…

Probability · Mathematics 2025-01-03 Ryoji Takano

We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…

Probability · Mathematics 2022-05-24 Shuo Yan

In this paper we establish the large deviation principle for the stochastic quasi-geostrophic equation in the subcritical case with small multiplicative noise. The proof is mainly based on the stochastic control and weak convergence…

Probability · Mathematics 2013-05-22 Wei Liu , Michael Röckner , Xiangchan Zhu

Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…

Probability · Mathematics 2007-05-23 Zach Dietz , Sunder Sethuraman

Large deviation principle by the weak convergence approach is established for the stochastic nonlinear Schrodinger equation in one-dimension and as an application the exit problem is investigated.

Analysis of PDEs · Mathematics 2019-11-04 Parisa Fatheddin , Zhaoyang Qiu

Using the large-deviation formalism, we study the statistics of current fluctuations in a diffusive nonequilibrium quantum spin chain. The boundary-driven XX chain with dephasing consists of a coherent bulk hopping and a local dissipative…

Statistical Mechanics · Physics 2014-04-25 Marko Znidaric

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

A Freidlin-Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and…

Probability · Mathematics 2020-03-10 Xiaobin Sun , Ran Wang , Lihu Xu , Xue Yang

We present a convergence result for solutions of the vector-valued Allen-Cahn Equation. In the spirit of the work of Luckhaus and Sturzenhecker we establish convergence towards a distributional formulation of multi-phase mean-curvature flow…

Analysis of PDEs · Mathematics 2016-09-26 Tim Laux , Thilo Simon

We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in…

Probability · Mathematics 2025-02-05 Xiaoyu Yang , Yong Xu

The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…

Probability · Mathematics 2017-08-25 Arnab Ganguly

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…

Dynamical Systems · Mathematics 2017-09-15 Getachew K. Befekadu

We study small noise large deviation asymptotics for stochastic differential equations with a multiplicative noise given as a fractional Brownian motion $B^H$ with Hurst parameter $H>\frac12$. The solutions of the stochastic differential…

Probability · Mathematics 2020-06-18 Amarjit Budhiraja , Xiaoming Song

In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $\alpha\in(0,1)$. First, the well-posedness and (limited) smoothing…

Numerical Analysis · Mathematics 2019-06-18 Qiang Du , Jiang Yang , Zhi Zhou

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.

Probability · Mathematics 2007-05-23 F. Klebaner , R. Liptser

We prove the large deviation principle for the law of the solutions to a class of parabolic semilinear stochastic partial differential equations driven by multiplicative noise, in $C\big([0,T]:L^\rho(D)\big)$, where $D\subset {\mathbb R}^d$…

Probability · Mathematics 2020-10-28 Leila Setayeshgar

In this work, we present a second-order nonuniform time-stepping scheme for the time-fractional Allen-Cahn equation. We show that the proposed scheme preserves the discrete maximum principle, and by using the convolution structure of…

Numerical Analysis · Mathematics 2022-01-05 Hong-lin Liao , Tao Tang , Tao Zhou

We study the stochastic Allen-Cahn equation driven by a noise term with intensity $\sqrt{\varepsilon}$ and correlation length $\delta$ in two and three spatial dimensions. We study diagonal limits $\delta, \varepsilon \to 0$ and describe…

Probability · Mathematics 2016-06-02 Martin Hairer , Hendrik Weber