%0 Journal Article
%T 一类非线性SDE的解的存在唯一性及其显式解<br>Existence and Uniqueness of Solutions for a Class of Nonlinear SDE and Their Explicit So-lutions
%A 邹峰
%A 陈倩
%A 连保胜
%J Advances in Applied Mathematics
%P 2927-2932
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.115311
%X 本文运用Holder不等式、Gronwall不等式等基础工具，从简单的常系数线性随机微分方程出发，通过取积分因子，将非线性随机微分方程变成确定性的微分方程，再经过适当变换，得到它的解，以此证明解的存在性和唯一性。<br />
This paper uses Holder inequality, Gronwall inequality and other basic tools, starting from a simple linear stochastic differential equation with constant coefficients, by taking the integral factor, the nonlinear stochastic differential equation is transformed into a deterministic differential equation, and then through appropriate transformation, we get its solution, so as to prove the existence and uniqueness of the solution.
%K 非线性随机微分方程，解的存在性和唯一性，Holder不等式，Gronwall不等式，显式解<br>Nonlinear Stochastic Differential Equations
%K Existence and Uniqueness of Solutions
%K Holder Inequality
%K Gronwall Inequality
%K Explicit Solution
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=51831