# 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

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.

[1] 孙清华, 孙昊 (2004) 随机过程内容、方法与技巧. 华中科技大学出版社, 武汉, 206-216.

[2] 田铮, 秦超英 (2007) 随机过程与应用. 科学出版社, 北京, 97-100.

[3] 刘嘉焜, 王公恕 (2001) 应用随机过程(第二版). 科学出版社, 北京, 218-238.

[4] 林元烈 (2001) 应用随机过程. 清华大学出版社, 北京, 288-312.

[5] 李顺萍 (2010) 随机微分方程样本广义解. 硕士论文, 华中科技大学, 王湘君.

[6] Evans, L.C. (1999) An introduction to stochastic differential equations (Version 1.2). Department of Mathematics University of California, Berkeley, 81-95.

[7] Gillespie, I.I. and Skorohod, A.V. (1972) Stochastic differential equations. Springer, Berlin.

[8] Arnold, L. (1974) Stochastic differential equations: Theory and applications. Wiley, Hoboken.

[9] 王子亭, 李萍 (2009) 分类随机微分方程的一般解. 中国石油大学学报: 自然科学版, 1, 167-170.

[10] 金治明 (1985) 一类随机微分方程的解法. 湖南数学年刊, 1, 1-8.

Top