TY - JOUR

T1 - Backward Euler–Maruyama method for the random periodic solution of a stochastic differential equation with a monotone drift

AU - Wu, Yue

N1 - This work is supported by the Alan Turing Institute for funding this work under EPSRC Grant EP/N510129/1 and EPSRC for funding though the Project EP/S026347/1, titled "Unparameterised multimodal data, high order signatures, and the mathematics of data science."

PY - 2022/5/11

Y1 - 2022/5/11

N2 - In this paper, we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler–Maruyama method. The existence of the random periodic solution is shown as the limit of the pull-back flows of the SDE and the discretized SDE, respectively. We establish a convergence rate of the strong error for the backward Euler–Maruyama method with order of convergence 1/2.

AB - In this paper, we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler–Maruyama method. The existence of the random periodic solution is shown as the limit of the pull-back flows of the SDE and the discretized SDE, respectively. We establish a convergence rate of the strong error for the backward Euler–Maruyama method with order of convergence 1/2.

KW - random periodic solution

KW - stochastic differential equations

KW - monotone drift

KW - backward Euler-Maruyama method

U2 - 10.1007/s10959-022-01178-w

DO - 10.1007/s10959-022-01178-w

M3 - Article

SN - 0894-9840

VL - 36

SP - 605

EP - 622

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 1

ER -