一类非线性随机微分方程的统计性质

STATISTICAL PROPERTIES OF A CLASS OF NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS

本文研究了一类分数布朗运动(fBm)驱动的非线性随机微分方程解的统计性质的问题.利用Lamperti变换的方法,可以把该方程转换为分数布朗运动驱动的线性随机微分方程,从而可以利用高斯过程的相关性质,获得该非线性随机微分方程解的期望和方差.在特殊情况下,该非线性随机微分方程的解是分数Cox-Ingersoll-Ross(fCIR)过程,该方法可以推广到计算分数Cox-Ingersoll-Ross(fCIR)过程的相关统计性质.

In this paper,we study the problem of the statistical properties of solutions for a class of nonlinear stochastic differential equations driven by fractional Brownian motion(f Bm).By using the Lamperti transform method,the equation can be transformed into a linear stochastic differential equation driven by fractional Brownian motion,and the expectation and variance of the solution of the nonlinear stochastic differential equation can be obtained by using the related properties of Gaussian process.In special cases,the solution of the nonlinear stochastic differential equation is a fractional Cox-Ingersoll-Ross(fCIR)process,and the method can be applied to calculate the relevant statistical properties of the fractional Cox-Ingersoll-Ross(fCIR)process.