Markov调制的随机泛函微分方程解的渐近性质

王琳

数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 711-726.

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数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 711-726. DOI: 10.12386/A2013sxxb0071
论文

Markov调制的随机泛函微分方程解的渐近性质

    王琳
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Asymptotic Properties of a Class of Nonlinear Stochastic Functional Differential Equations with Markovian Switching

    Lin WANG
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文章历史 +

摘要

本文主要给出了一个新的条件,这个条件能够确保Markov调制的非线性随机泛函微分方程存在唯一解,同时这个解矩有界, 时间平均矩有界.这个条件只是以局部Lipschitz条件为前提, 线性增长条件不再是前提条件.本文的方程系数可以为多项式增长或被多项式增长限制.

Abstract

The main aim of this paper is to give a new condition which assures a class of nonlinear stochastic functional differential equations with Markovian switching have a unique solution and at the same time the moment, the moment average in time of this solution are bounded. The new condition is under the assumption of the local Lipschitz condition but neither the linear growth condition. Here we allow the coefficients of these equations are polynomial or are controlled by polynomial growth speed. An example is also given for illustration.

关键词

矩有界 / 广义伊藤公式 / Brown运动 / Markov调制

Key words

moment boundedness / generalized Itô / formula / Brownian motion / Markovian switching

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王琳. Markov调制的随机泛函微分方程解的渐近性质. 数学学报, 2013, 56(5): 711-726 https://doi.org/10.12386/A2013sxxb0071
Lin WANG. Asymptotic Properties of a Class of Nonlinear Stochastic Functional Differential Equations with Markovian Switching. Acta Mathematica Sinica, Chinese Series, 2013, 56(5): 711-726 https://doi.org/10.12386/A2013sxxb0071

参考文献

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基金

国家自然科学基金资助项目(11201083); 广东工业大学博士启动基金资助项目(093054)

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