推广的Bessel过程的L~p估计

随机微分方程dX_t=(δf~2(t)-h(t)X_t)dt+2f(t) │X_t│～(1/2)dBt,(X_0=x,δ>0)的解X_t是一种推广的δ(δ>0)维Bessel过程.文章对于任意停时τ给出了‖sup0≤t≤τη(t)X_t‖p的L~p估计,其中η:R_+→R_+是一个R+上的可微函数,而且满足微分方程dη/dt-h(t)η=-η~2f~2(t),η(0)=1.

The Lp Estimation of Generalized Bessel Process

The solution Xt of stochastic differential equation dX_t=(δf~2(t)-h(t)X_t)dt+2f(t)|X_t|～(1/2)dB_t,(X0=x,δ>0)is a kind of generalized process of δ(δ>0)dimension.For arbitrary Stopping time,the thesis gives a Lpestimation for ‖sup0≤t≤τη(t)X_t‖p,here η:R_+→R_+ is a function of R+,and satisfy differentiable equation dη/dt-h(t)η=-η~2f~2(t),η(0)=1.