超O．U．过程的占位时过程的极限性质  

Asymptotic Properties of an Occupation Time Process Associated with Some Super Ornstein Uhlenbeck Process

作　　者：鲍玉芳[1] 

机构地区：[1]北京邮电大学基础科学部

出　　处：《北京邮电大学学报》1996年第4期53-56,共4页Journal of Beijing University of Posts and Telecommunications

基　　金：邮电部青年科研基金

摘　　要：研究了分枝特征为ψ（ｚ）＝ｚ１＋β，０＜β＜１，底过程为Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ（Ｏ．Ｕ．）过程的超过程的占位时过程（Ｙｔ）ｔ≥０当ｔ→∞时极限行为．证明了对任意的维数ｄ，如果底过程是暂留的，则超Ｏ．Ｕ．过程的总的占位时是Ｐλ－ａ．ｓ．有限的；如果底过程是常返的，则Ｙｔ／βｔＰｍλ－ａ．ｓ．We studied the asymptoic properties of an occupation time process associated with some super Ornstein Uhlenbeck process as t→∞.We proved that the total occupation time is finite P λ-a.s.when the underlying process is transient, and we also proved that β -1 tY t converges vaguly to mλ P mλ -a.s.when the underlying process is recurrent, the above results are independent with dimension d.

关 键 词：极限定理 超OU过程 占位时过程 

分 类 号：O211.4[理学—概率论与数理统计]