相关论文: Convergence of a stochastic particle approximation…

The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the L\'evy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary…

Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…

For a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H> \frac12$ it is known that the classical Euler scheme has the rate of convergence $2H-1$. In this paper we introduce a new numerical…

We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…

In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…

In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…

In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…

We introduce a semi-implicit Milstein approximation scheme for some class of non-colliding particle systems modeled by systems of stochastic differential equations with non-constant diffusion coefficients. We show that the scheme converges…

This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…

We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…

Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…

This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. Such systems are described by second order stochastic differential-algebraic equations involving an implicitly…

In this paper, we analyse the rate of convergence of a system of $N$ interacting particles with mean-field rank based interaction in the drift coefficient and constant diffusion coefficient. We first adapt arguments by Kolli and Shkolnikhov…

In this paper, we are concerned with a operator splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Levy noise. More specifically, using a variant of classical Kruzkov's…

In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous.

In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…

The Euler scheme is one of the standard schemes to obtain numerical approximations of stochastic differential equations (SDEs). Its convergence properties are well-known in the case of globally Lipschitz continuous coefficients. However, in…

In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate $\alpha$-stable processes (including cylindrical ones) with $\alpha \in (1,2)$. We first establish a quantitative estimate for the…

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…