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