Numerical solutions of neutral stochastic functional differential equations with Markovian switching

Abstract

Until now, the theories about the convergence analysis, the almost surely and mean square exponential stability of the numerical solution for neutral stochastic functional differential equations with Markovian switching (NSFDEwMSs) have been well established, but there are very few research works concentrating on the stability in distribution of numerical solution. This paper will pay attention to the stability in distribution of numerical solution of NSFDEwMSs. The strong mean square convergence analysis is also discussed.

Euler-Maruyama Method for Regime Switching Stochastic Differential Equations with Hölder Coefficients

“…Numerical schemes for regime switching SDEs therefore have become an active area since the pioneer work by Yuan and Mao [31] with numerous results on various aspects [11,12,15,16,19,22,23,24,25,27,28,32,33]. See, for instance, [31] for Euler-Maruyama method, [24] for weak Euler-Maruyama method, [22] for tamed-Euler method, [23] for Milstein-type algorithm, [11,32] for stability of numerical approximations, [33] for stabilization of numerical solutions, [15] for approximation of invariant measures, [25,27] for numerical scheme for state-dependent switching systems, [28] for scheme for hybrid systems with jumps, [16] for approximation of delayed hybrid systems (see also [12]). However, most of the aforementioned works (except [19], to the best of our knowledge, which focuses on somewhat specific models) require the global or local Lipschitz conditions for the drift and diffusion coefficients despite of a vital fact that many models in reality violate these conditions.…”