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Fixed Points and Stability of Neutral Stochastic Differential Equations with Variable Delays

Author: ZhangYouCun
Tutor: LuoJiaoWan
School: Guangzhou University
Course: Probability Theory and Mathematical Statistics
Keywords: stability fixed points neutral stochastic differential equation variabledelays
CLC: O211.63
Type: Master's thesis
Year: 2013
Downloads: 13
Quote: 0
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Abstract


By means of Banach’s fixed points theory, in this paper we study two class ofneutral stochastic differential equations with variable delays and give conditions toensure that the zero solution is asymptotically mean square stable. The conditions ofcoefficient function is weakened and these conditions do not require the boundednessof delays, Some well-known results are improved and generalized.The frame of this paper is following:Chapter1, Introduce the history background of stochastic process and stochastic diff-erential equations.Chapter2, Introduce the research methods of stochastic differential equations and thepreliminary knowledge to this paper.Chapter3, we study the stability of a class of neutral stochastic delays differentialequations and generalize some well-known results.Chapter4, we study the stability of a class of neutral nonlinear stochastic differentialequations with variable delays and improved some well-known results.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Random process > Stochastic differential equation
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