Related papers: Large deviations of conservative stochastic partia…
Large and moderate deviation principles are proved for Engel continued fractions, a new type of continued fraction expansion with non-decreasing partial quotients in number theory.
In this paper, a large deviation principle for the strong solution of the p-Laplace equation on unbounded domain driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment…
In this work we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for so- lutions of the…
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…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive…
The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction…
Complex solutions to squared Bessel SDEs appear naturally in relation to Schramm-Loewner evolutions. We prove a large deviation principle for such solutions as the dimension parameter tends to $-\infty$.
This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally…
We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics…
For a heat equation with memory driven by a L\'evy-type noise we establish the existence of a unique solution. The main part of the article focuses on the Freidlin-Wentzell large deviation principle of the solutions of heat equation with…
It is well known that symplectic methods have been rigorously shown to be superior to non-symplectic ones especially in long-time computation, when applied to deterministic Hamiltonian systems. In this paper, we attempt to study the…
A Boussinesq model for the Benard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for…
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…