二参数ORNSTEIN-UHLENBECK过程在射线上的导出过程

PROCESSES INDUCED BY AN ORNSTEIN-UHLENBECK PROCESS WITH TWO PARAMETERS ON THE RAYS

本文证明了二参数ORNSTEIN-UHLENBECK过程在射线上导出的过程是马氏过程,并求出了它的转移密度。同时证明了它为oup1的充要条件及它是弱平稳过程的充要条件。

Let X(x,t)=e^(-as-βt)[X_0+σintegral from 0 to 3 integral from 0 to t e^(αa_βb)dw (a,b)] be an Ornstein-Uhlenbeck Process with two parameters (oup2). Let l: t=λs+T(s≥0) be a ray, and λ and c two nonnegative constants. Y=X(s,λs+c), s≥0, is the process induced by X(s, t) on the ray l. Y is a Marker Process and its transition density is calculated. It is proved that Y is oup_1 if and only if λ=0, c>0, and Y is a weakly stationary Process if and only if λ=0, c=(In(σ~2+4αβEX_0~2)-2lnσ)/2β