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Article

A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models

by
Yang Li
*,
Taitao Feng
,
Yaolei Wang
and
Yifei Xin
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(6), 588; https://doi.org/10.3390/math9060588
Submission received: 30 January 2021 / Revised: 8 March 2021 / Accepted: 9 March 2021 / Published: 10 March 2021
(This article belongs to the Special Issue Advances in Applications of Probability Theory and Stochastic Processes)
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Abstract

In this paper, we propose a new weak order 2.0 numerical scheme for solving stochastic differential equations with Markovian switching (SDEwMS). Using the Malliavin stochastic analysis, we theoretically prove that the new scheme has local weak order 3.0 convergence rate. Combining the special property of Markov chain, we study the effects from the changes of state space on the convergence rate of the new scheme. Two numerical experiments are given to verify the theoretical results.
Keywords: weak order 2.0 scheme; markovian switching; malliavin calculus weak order 2.0 scheme; markovian switching; malliavin calculus

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MDPI and ACS Style

Li, Y.; Feng, T.; Wang, Y.; Xin, Y. A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models. Mathematics 2021, 9, 588. https://doi.org/10.3390/math9060588

AMA Style

Li Y, Feng T, Wang Y, Xin Y. A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models. Mathematics. 2021; 9(6):588. https://doi.org/10.3390/math9060588

Chicago/Turabian Style

Li, Yang, Taitao Feng, Yaolei Wang, and Yifei Xin. 2021. "A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models" Mathematics 9, no. 6: 588. https://doi.org/10.3390/math9060588

APA Style

Li, Y., Feng, T., Wang, Y., & Xin, Y. (2021). A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models. Mathematics, 9(6), 588. https://doi.org/10.3390/math9060588

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