两类随机微分方程的P-期望概自守型温和解

发布时间：2018-02-27 00:05

本文关键词： 随机微分方程均方渐近概自守温和解 p-期望伪概自守温和解压缩映射原理 Schauder不动点定理　出处：《哈尔滨理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：随机微分方程是为解决某些具有随机现象的问题而建立起来的一类数学模型,是微分方程的延伸,其被广泛地应用于数学以外的很多领域中。本文主要对两类随机微分方程的p-期望概自守型温和解的存在性和唯一性进行研究:1.首先利用均方渐近概自守随机过程的定义和均方概自守随机过程值域的性质以及Cauchy-Schwarz不等式,给出均方渐近概自守随机过程值域的闭包包含其相应的均方概自守随机过程的值域这一基本性质。然后结合Lipschitz条件,并利用均方渐近概自守随机过程值域的这一性质研究均方渐近概自守随机过程的可复合性。最后利用压缩映射原理,?Ito随机积分等距公式,卷积族的指数稳定性,讨论一类具有延迟的随机微分方程的均方渐近概自守温和解的存在性和唯一性。2.研究一类随机积分微分方程的p-期望伪概自守温和解的存在唯一性。首先在该类方程预解算子族指数稳定和Lipschitz条件及其它适当的假设条件下,利用p-期望伪概自守随机过程的概念和一些基本性质,结合Lebesgue控制收敛定理,压缩映射原理,?Ito随机积分性质,讨论该类随机方程的p-期望伪概自守温和解的存在性和唯一性。然后利用Schauder不动点定理,?Ito随机积分性质,Arzela-Ascoli引理,H?lder不等式,讨论在弱于Lipschitz条件下该类方程的p-期望伪概自守温和解的存在性。
[Abstract]:Stochastic differential equation is a kind of mathematical model established to solve some problems with random phenomena. It is an extension of differential equation. It is widely used in many fields outside mathematics. In this paper, we study the existence and uniqueness of the p- expected almost self-propriety temperature solutions for two kinds of stochastic differential equations. Firstly, we use the mean square asymptotically almost self-conformal random overpass to study the existence and uniqueness of the solution. The definition of the mean square and the properties of the range of random processes and the Cauchy-Schwarz inequality. In this paper, we give the basic property that the closure of the range of mean square asymptotically almost autosomorphic random process contains the range of the corresponding mean square almost autosomorphic random process, and then combine with the Lipschitz condition, By using the property of the range of mean square asymptotically almost automorphic stochastic processes, the compounding property of mean-square asymptotically almost self-preserving stochastic processes is studied. Finally, the contraction mapping principle is used. Ito random integral equidistant formula, exponential stability of convolution family, In this paper, we discuss the existence and uniqueness of mean-square asymptotically almost self-preserving temperature solutions for a class of stochastic differential equations with delay. 2. We study the existence and uniqueness of p-expectation pseudo-almost self-preserving temperature solutions for a class of stochastic integrodifferential equations. Exponential stability, Lipschitz condition and other appropriate assumptions of the family of resolvent operators for the equation, By using the concept and some basic properties of p- expected pseudo-almost automorphic stochastic process, combined with the convergence theorem of Lebesgue control, the principle of contraction mapping is discussed. In this paper, we discuss the existence and uniqueness of the p-expectation pseudo-almost self-preserving temperature solution for this kind of stochastic equation by Ito stochastic integral property. Then we use the Schauder fixed point theorem to discuss the existence and uniqueness of the p-expectation pseudo-almost self-preserving temperature solution. Ito random integral properties Arzela-Ascoli Lemma H? In this paper, we discuss the existence of p-expectation pseudo-almost self-preserving temperature solutions for this class of equations under weak Lipschitz conditions.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.63

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