發(fā)布時間：2018-03-17 23:06

  本文選題：隨機微分方程　切入點：均方漸近概周期解　出處：《哈爾濱理工大學》2015年碩士論文　論文類型：學位論文

【摘要】：隨機微分方程是在解決某些具有隨機現(xiàn)象的問題而建立起來的一類方程。隨機微分方程在諸多領域有著廣泛的應用，而隨機微分方程的均方概周期類型解的存在性和唯一性在隨機過程理論和概周期型函數(shù)理論的基礎上更加具有研究意義。本文主要討論了兩類隨機微分方程均方漸近概周期解的存在性和唯一性。 全文內(nèi)容如下： 第一部分介紹了目前概周期型函數(shù)理論和隨機微分方程理論的背景知識和主要研究成果，以及今后的發(fā)展趨勢。 第二部分研究了一類非線性隨機微分方程的均方漸近概周期解的存在唯一性。首先給出有關概周期隨機過程的部分理論知識，介紹了一類一致漸近穩(wěn)定的C0半群的有關知識，然后討論了聯(lián)合連續(xù)函數(shù)的漸近概周期性質(zhì)，利用該性質(zhì)、Fubini定理、Holder不等式以及Banach不動點原理討論了該方程均方漸近概周期解的存在唯一性。 第三部分在第二部分的理論基礎上，討論了一類非自治隨機微分方程的均方漸近概周期解的存在唯一性。首先給出解決該類方程所需的理論知識和相關內(nèi)容，然后介紹了一類算子開方族的基本概念，，再應用Fubini定理、Holder不等式以及Banach不動點原理討論了該類方程均方漸近概周期解的存在唯一性。
[Abstract]:Stochastic differential equation is a kind of equation which is established in solving some problems with random phenomena. Stochastic differential equation is widely used in many fields. However, the existence and uniqueness of mean square almost periodic type solutions of stochastic differential equations are of great significance on the basis of stochastic process theory and almost periodic function theory. In this paper, we mainly discuss two kinds of stochastic differential equations. Existence and uniqueness of asymptotically almost periodic solutions. The text reads as follows:. The first part introduces the background knowledge and main research results of almost periodic function theory and stochastic differential equation theory, as well as the development trend in the future. In the second part, we study the existence and uniqueness of mean-square asymptotically almost periodic solutions for a class of nonlinear stochastic differential equations. Firstly, we give some theoretical knowledge about almost periodic stochastic processes, and introduce some knowledge about a class of uniformly asymptotically stable C _ 0 Semigroups. Then the asymptotically almost periodic property of joint continuous function is discussed and the existence and uniqueness of the mean square asymptotic almost periodic solution of the equation are discussed by using the Banach fixed point principle and the Fubini theorem. In the third part, on the basis of the theory of the second part, we discuss the existence and uniqueness of the mean square asymptotic almost periodic solution for a class of nonautonomous stochastic differential equations. Then we introduce the basic concept of a class of open square family of operators, and discuss the existence and uniqueness of mean square asymptotically almost periodic solutions of this class of equations by using Fubini theorem and Banach fixed point principle.
【學位授予單位】：哈爾濱理工大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O211.63

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相關博士學位論文 前1條

1 曹俊飛;隨機泛函微分方程的概周期性及概自守性研究[D];華南理工大學;2012年

本文編號：1626885