一类非线性SDE的解的存在唯一性及其显式解

Existence and Uniqueness of Solutions for a Class of Nonlinear SDE and Their Explicit So-lutions

摘要: 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。

Abstract: 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.