摘要
本文讨论扩散过程样本的H lder连续性.在局部Lipschitz条件下,我们证明了扩散过程样本有类似于Brown运动样本一样的H lder连续性.进一步,我们还讨论了扩散过程样本的象与图集的Hausdroff维数.
In this paper ,we consider the Holder continuity of diffrsion process. We proved following results. Let be solution of the following equations :where B(t) =B1 (t), ...,Bd(t) is Brown Motion if for any T>0 ,there exists KT<∞,for all |x|≤T, |y|≤T, x, y ∈RN ,0≤t≤T, we have |α(t , x) - α (t , y)|2 +|β (t , x) -β (t , y)|2≤KT |x-y|2. Then for any and T>0, there exist functions fT(ω)<∞,a ,s and uT(ω)>0 ,a. s such that for all 0≤s<t≤T,t-s≤uT (ω),|Xt(ω)-Xs(ω)|≤fT(ω)| t- s|λwhere α (t,x)=(αij (t , x), 1≤i≤N,1≤j≤d), β(t,x) = (β1(t,x)...,,βN(t,x)),u=( u1,..., uD ) ∈RD,v∈RD, then u-v= (u1-v1, ... ,uD-vD), Furthermore, we discussed the Hausdroff dimensions of the diffusion processes.
出处
《湖南师范大学自然科学学报》
CAS
1995年第2期13-18,共6页
Journal of Natural Science of Hunan Normal University
基金
国家青年自然科学基金
关键词
扩散过程
连续性
随机过程
diffusion process
Brown motion
Holder continuity
Hausdroff dimension