# 几种随机微分方程解的存在性与唯一性The Existence and Uniqueness of Solution for Some Kinds of Stochastic Differential Equations

DOI: 10.12677/AAM.2015.41005, PDF, HTML, XML, 下载: 2,815  浏览: 10,162  国家自然科学基金支持

Abstract: Stochastic differential equation (SDE) is a relatively new discipline branch linking the deterministic and non-deterministic phenomenon [1]. The method of studying SDE is proceeded from two aspects of qualitative and quantitative. Qualitative aspect is studying the existence, uniqueness and stability of the solution of SDE; and quantitative aspect is concerning the solving method and the statistical characteristics of the solving process [2]. In order to carry out the following proof, the thesis presents some basic theory knowledge about stochastic differential equation. By means of doing transforms, we obtain the expressions solution of SDE with the help of the formula , and thus we show the existence of the SDE. And finally, we prove the uniqueness of the solution of the SDE by utilizing the Cauchy-Schwarz inequality, the Lipschitz condition and the Gronwall’s lemma.

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