A note on the asymptotic stability of the semi-discrete method for stochastic differential equations
A note on the asymptotic stability of the semi-discrete method for stochastic differential equations
Abstract We study the asymptotic stability of the semi-discrete (SD) numerical method for the approximation of stochastic differential equations. Recently, we examined the order of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi mathvariant="script">ℒ</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> {\mathcal{L}^{2}} -convergence of the truncated SD method and showed that it can be arbitrarily close to <m:math …