Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations
For test equations that are Itô stochastic differential equations (SDE) of the form \(dx(t)= \alpha x(t)dt+\mu x(t)dW(t)\) (where \(\alpha\), \(\mu\) are constants) whose mean-square stability is known, a theorem is proved that specifies step-sizes for which the author's improved split-step theta method (ISST) is mean-square stable when applied to these test equations. Conditions are identified and proved under which ISST is exponentially mean-square stable when applied to nonautonomous systems of SDE of the form \(dx(t)= f (t,x(t))dt+ g(t, x(t)) dW(t)\). Numerical results for two examples are given that demonstrate the accuracy of the theorems.
scientific article; zbMATH DE number 6855826
scientific article