The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching

Abstract In this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then,...

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Main Authors:	Yanan Jiang, Liangjian Hu, Jianqiu Lu
Format:	Article
Language:	English
Published:	SpringerOpen 2020-11-01
Series:	Advances in Difference Equations
Subjects:	Stochastic θ method SDEs with Markovian switching Numerical solutions Stationary distribution
Online Access:	https://doi.org/10.1186/s13662-020-03129-3

id	doaj-58e90f7d1ad54247bbb1bdb4d1020191
record_format	Article
spelling	doaj-58e90f7d1ad54247bbb1bdb4d10201912020-11-29T12:20:28ZengSpringerOpenAdvances in Difference Equations1687-18472020-11-012020112510.1186/s13662-020-03129-3The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switchingYanan Jiang0Liangjian Hu1Jianqiu Lu2College of Information Science and Technology, Donghua UniversityDepartment of Statistics, Donghua UniversityDepartment of Statistics, Donghua UniversityAbstract In this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then, the convergence of numerical stationary distribution to the underlying one is discussed. Numerical simulations are conducted to support the theoretical results.https://doi.org/10.1186/s13662-020-03129-3Stochastic θ methodSDEs with Markovian switchingNumerical solutionsStationary distribution
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yanan Jiang Liangjian Hu Jianqiu Lu
spellingShingle	Yanan Jiang Liangjian Hu Jianqiu Lu The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching Advances in Difference Equations Stochastic θ method SDEs with Markovian switching Numerical solutions Stationary distribution
author_facet	Yanan Jiang Liangjian Hu Jianqiu Lu
author_sort	Yanan Jiang
title	The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching
title_short	The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching
title_full	The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching
title_fullStr	The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching
title_full_unstemmed	The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching
title_sort	stochastic θ method for stationary distribution of stochastic differential equations with markovian switching
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2020-11-01
description	Abstract In this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then, the convergence of numerical stationary distribution to the underlying one is discussed. Numerical simulations are conducted to support the theoretical results.
topic	Stochastic θ method SDEs with Markovian switching Numerical solutions Stationary distribution
url	https://doi.org/10.1186/s13662-020-03129-3
work_keys_str_mv	AT yananjiang thestochasticthmethodforstationarydistributionofstochasticdifferentialequationswithmarkovianswitching AT liangjianhu thestochasticthmethodforstationarydistributionofstochasticdifferentialequationswithmarkovianswitching AT jianqiulu thestochasticthmethodforstationarydistributionofstochasticdifferentialequationswithmarkovianswitching AT yananjiang stochasticthmethodforstationarydistributionofstochasticdifferentialequationswithmarkovianswitching AT liangjianhu stochasticthmethodforstationarydistributionofstochasticdifferentialequationswithmarkovianswitching AT jianqiulu stochasticthmethodforstationarydistributionofstochasticdifferentialequationswithmarkovianswitching
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The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching

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