Invariant measure of the backward Euler method for stochastic differential equations driven by α$$ \alpha $$‐stable process

Abstract

The backward Euler method is employed to approximate the invariant measure of a class of stochastic differential equations (SDEs) driven by ‐stable processes. The existence and uniqueness of the numerical invariant measure are proved. Then the numerical invariant measure is shown to converge to the underlying invariant measure. Numerical examples are provided to demonstrate the theoretical results.