Article Contents
Article Contents

# The truncated Milstein method for super-linear stochastic differential equations with Markovian switching

• * Corresponding author: Qian Guo

The second author is supported by NSFC of China (No:11871343). The third author is supported by NSFC of China (No:11971303)

• In this paper, to approximate the super-linear stochastic differential equations modulated by a Markov chain, we investigate a truncated Milstein method with convergence order 1 in the mean-square sense. Under Khasminskii-type conditions, we establish the convergence result by employing a relationship between local and global errors. Finally, we confirm the convergence rate by a numerical example.

Mathematics Subject Classification: Primary: 60H35; Secondary: 65C30.

 Citation:

• Figure 1.  The strong convergence order at the terminal time $T = 1$. The red dashed line is the reference line with the slope of 1

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