On explicit tamed Milstein-type scheme for stochastic differential equation with Markovian switching

Abstract

We propose a new tamed Milstein-type scheme for stochastic differential equation with Markovian switching when drift coefficient is assumed to grow super-linearly. The strong rate of convergence is shown to be equal to 1.0 under mild regularity (e.g. once differentiability) requirements on drift and diffusion coefficients. Novel techniques are developed to tackle two-fold difficulties arising due to jumps of the Markov chain and the reduction of regularity requirements on the coefficients.