A Note on Explicit Milstein-Type Scheme for Stochastic Differential Equation with Markovian Switching

2019/09/17 by Kumar, Chaman, Kumar, Tejinder
#FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1909.07882

Abstract

An explicit Milstein-type scheme for stochastic differential equation with Markovian switching is derived and its strong convergence in L²-sense is established without using Itô-Taylor expansion formula. Rate of strong convergence is shown to be equal to 1.0 under the assumptions that coefficients satisfy mild regularity conditions. More precisely, coefficients are assumed to be only once differentiable which are more relaxed conditions than those made in existing literature.

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