Related papers: Large Deviation Principle for Neutral Type Mckean-…
In this paper, we consider a kind of fully coupled slow fast motion, in which the slow variable satisfies the non Lipschitz condition. We prove that the stochastic flow of the slow variable exists and moreover, satisfies the large deviation…
We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…
An explicit first-order drift-randomized Milstein scheme for a regime switching stochastic differential equation is proposed and its bi-stability and rate of strong convergence are investigated for a non-differentiable drift coefficient.…
We present the particle method for simulating the solution to the path-dependent McKean-Vlasov equation, in which both the drift and the diffusion coefficients depend on the whole trajectory of the process up to the current time t, as well…
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…
We investigate the conditional McKean-Vlasov stochastic differential equations with jumps and Markovian regime-switching. We establish the strong wellposedness using L2-Wasser-stein distance on the Wasserstein space. Also, we establish the…
We present a large deviation principle for some stochastic evolution equations with jumps which depend on two small parameters, when the viscosity parameter {\epsilon} tends to zero more quickly than the homogenization's one…
We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant…
The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…
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…
We demonstrate the large deviation principle in the small noise limit for the mild solution of stochastic evolution equations with monotone nonlinearity. A recently developed method, weak convergent method, has been employed in studying the…
The purpose of this paper is to study some properties of solutions to one dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth conditions on the coefficients. Taking inspiration…
In this work, we establish the small-noise asymptotic behaviour (namely, the functional law of large numbers and the large deviation principle) for multi-scale McKean--Vlasov diffusions with super-linear kernels. In this setting, the…
McKean-Vlasov stochastic differential equations (MVSDEs) describe systems whose dynamics depend on both individual states and the population distribution, and they arise widely in neuroscience, finance, and epidemiology. In many…
We present a Lyapunov type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature most results concerning existence and uniqueness are obtained under…
Since T. Lyons invented rough path theory, one of its most successful applications is a new proof of Freidlin-Wentzell's large deviation principle for diffusion processes. In this paper we extend this method to the case of pinned diffusion…
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.
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.
We establish an existence result of a solution to a class of probability measure-valued equations, whose solutions can be associated with stationary distributions of many McKean-Vlasov diffusions with gradient-type drifts. Coefficients of…
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…