Related papers: An Explicit Euler-type Scheme for L\'evy-driven SD…
We derive strong Lp convergence rates for the Euler-Maruyama schemes of Levy-driven SDE using a new dynamic cutting (DC) method with a time-dependent jump threshold. In addition, we present results from numerical simulations comparing the…
We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) driven by additive pure-jump L\'evy noise. In particular, we assume that the L\'evy process driving the SDE is…
We study the ergodic properties of a class of controlled stochastic differential equations (SDEs) driven by $\alpha$-stable processes which arise as the limiting equations of multiclass queueing models in the Halfin-Whitt regime that have…
In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by stochastic differential…
Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The…
We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to…
We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient.…
In this paper, we investigate the weak convergence rate of Euler-Maruyama's approximation for stochastic differential equations with irregular drifts. Explicit weak convergence rates are presented if drifts satisfy an integrability…
We study the rate of convergence of some recursive procedures based on some "exact" or "approximate" Euler schemes which converge to the invariant measure of an ergodic SDE driven by a L\'{e}vy process. The main interest of this work is to…
We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump L\'{e}vy processes. We prove a uniform in time propagation of chaos result, providing quantitative bounds on…
We are interested in the time discretization of stochastic differential equations with additive d-dimensional Brownian noise and L q -- L $\rho$ drift coefficient when the condition d $\rho$ + 2 q < 1, under which Krylov and R{\"o}ckner…
We introduce an explicit adaptive Milstein method for stochastic differential equations (SDEs) with no commutativity condition. The drift and diffusion are separately locally Lipschitz and together satisfy a monotone condition. This method…
In this paper we deal with pointwise approximation of solutions of stochastic differential equations (SDEs) driven by infinite dimensional Wiener process with additional jumps generated by Poisson random measure. The further investigations…
We consider controlled differential equations and give new estimates for higher order Euler schemes. Our proofs are inspired by recent work of A. M. Davie who considers first and second order schemes. In order to implement the general case…
This paper focuses on a stochastic system identification problem: given time series observations of a stochastic differential equation (SDE) driven by L\'{e}vy $\alpha$-stable noise, estimate the SDE's drift field. For $\alpha$ in the…
The paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and…
In this paper we investigate the convergence rate of Euler-Maruyama scheme for a class of stochastic differential delay equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In…
Over the last few decades, the numerical methods for stochastic differential delay equations (SDDEs) have been investigated and developed by many scholars. Nevertheless, there is still little work to be completed. By virtue of the novel…
In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.
We propose an effective explicit numerical scheme for simulating solutions of stochastic differential equations with confining superlinear drift terms, driven by multiplicative heavy-tailed L\'evy noise. The scheme is designed to prevent…