Convergence of jump-diffusion non-linear differential equation with phase semi-Markovian switching

Zhenting Hou; Jinying Tong; Zhenzhong Zhang

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Convergence of jump-diffusion non-linear differential equation with phase semi-Markovian switching

机译：相位半马氏切换的跳扩散非线性微分方程的收敛性

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摘要

Semi-Markov process (SMP) is a generalization of Markov process, which can overcome the restriction of the negative exponential distribution of the sojourn time at a state. In this paper, our focus is on the class of jump-diffusion stochastic delay differential equation with phase semi-Markovian switching. By employing the theta method, we prove that, for p ≥ 2, the pth-moment of discrete and continuous approximation solutions are stable, and the pth-moment error of the continuous approximation solution is convergent under some weak conditions. The techniques of proof are quite general and hence have the potential to be applied to other numerical models.

机译：半马尔可夫过程（SMP）是马尔可夫过程的一种概括，可以克服一个状态下停留时间的负指数分布的限制。在本文中，我们的重点是具有相半马氏切换的跳扩散随机时滞微分方程的类别。通过theta方法，我们证明，对于p≥2，离散和连续逼近解的pth矩是稳定的，并且在某些弱条件下，连续逼近解的pth矩误差是收敛的。证明技术是相当普遍的，因此有潜力应用于其他数值模型。

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来源
《Applied Mathematical Modelling》 |2009年第9期|3650-3660|共11页
作者
Zhenting Hou; Jinying Tong; Zhenzhong Zhang;
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作者单位

School of Mathematics, Central South University, Changsha, Hunan 410075, PR China;

School of Mathematics, Central South University, Changsha, Hunan 410075, PR China;

School of Mathematics, Central South University, Changsha, Hunan 410075, PR China Department of Economics, Carleton University, Ottawa, Canada;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
phase semi-markov process; the theta method; poisson process; convergence;

机译：相半马尔可夫过程;theta方法泊松过程收敛;

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5. CONVERGENCE AND SUPERCONVERGENCE OF NUMERICAL SOLUTIONS OF WEAKLY SINGULAR INTEGRAL AND DIFFERENTIAL EQUATIONS (GALERKIN, COLLOCATION, EIGENVALUES, EIGENVECTORS, SPLINES) [D] . LEBBAR, RACHID. 1986

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7. Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching [O] . Zhou Shaobo, Wu Fuke 2009

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Convergence of jump-diffusion non-linear differential equation with phase semi-Markovian switching

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