Work

Uniform in time convergence of numerical schemes for stochastic differential equations via strong exponential stability: Euler methods, split-step and tamed schemes

Year: 2025

Type: article

Abstract: We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent, discussed in the paper, necessary. Using such a criterion we then analyse the convergence properties of numerical methods for solutions of SDEs; we consider Explicit and Implicit Euler, split-step and (truncated) tamed Euler methods. In particular, we show that, under mild conditions on the coefficients of the SDE (locally Lipschitz and strictly monotone), these methods produce approximations of the law of the solution of the SDE that converge uniformly in time. The bounds we provide are non-asymptotic. The theoretical results are verified by numerical examples.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2025052

Authors: Letizia Angeli, Dan Crisan, Michela Ottobre

Institutions: Heriot-Watt University, Maxwell Institute for Mathematical Sciences, Imperial College London

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funder: Leverhulme Trust