DeepAI AI Chat
Log In Sign Up

Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme

by   Charles-Edouard Bréhier, et al.

We consider the long-time behavior of an explicit tamed Euler scheme applied to a class of stochastic differential equations driven by additive noise, under a one-sided Lipschitz continuity condition. The setting encompasses drift nonlinearities with polynomial growth. First, we prove that moment bounds for the numerical scheme hold, with at most polynomial dependence with respect to the time horizon. Second, we apply this result to obtain error estimates, in the weak sense, in terms of the time-step size and of the time horizon, to quantify the error to approximate averages with respect to the invariant distribution of the continuous-time process. We justify the efficiency of using the explicit tamed Euler scheme to approximate the invariant distribution, since the computational cost does not suffer from the at most polynomial growth of the moment bounds. To the best of our knowledge, this is the first result in the literature concerning the approximation of the invariant distribution for SDEs with non-globally Lipschitz coefficients using an explicit tamed scheme.


page 1

page 2

page 3

page 4


Strong convergence of an adaptive time-stepping Milstein method for SDEs with one-sided Lipschitz drift

We introduce explicit adaptive Milstein methods for stochastic different...

Approximation of solutions of DDEs under nonstandard assumptions via Euler scheme

We deal with approximation of solutions of delay differential equations ...

Analysis of a modified Euler scheme for parabolic semilinear stochastic PDEs

We propose a modification of the standard linear implicit Euler integrat...

Explicit approximation of the invariant measure for SDDEs with the nonlinear diffusion term

To our knowledge, the existing measure approximation theory requires the...

Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions

This paper studies the theoretical underpinnings of machine learning of ...

Euler scheme for approximation of solution of nonlinear ODEs under inexact information

We investigate error of the Euler scheme in the case when the right-hand...