超Ornstein-Uhlenbeck过程的占位时过程的绝对连续性

数学物理学报 ›› 1999, Vol. 19 ›› Issue (1): 94-100.

超Ornstein-Uhlenbeck过程的占位时过程的绝对连续性

(北京邮电大学 |北京 100088)

出版日期:1999-02-01 发布日期:1999-02-01

The Absolution Continuity for the Occupation Time of Super Ornstein Uhlenbeck Prosces

(Beijing University of Posts and Telecommunications 91^#, Beijing 100088)

Online:1999-02-01 Published:1999-02-01

摘要/Abstract

摘要：

证明了分支特征为ψ(z)=z²,底过程为d≤3 的暂留Ornstein-Uhlenbeck(O.U.)过程的超过程X_t的占位时过程Y(t)=∫^t₀ X_sds关于Lebesgue测度绝对连续,且其密度过程Y(t,x)关于t≥0,x∈R^d联合连续.

关键词: 超Ｏ．Ｕ．过程, 占位时过程, 绝对连续性．

Abstract:

In this article we proved that the occupation time process Y(t) =∫^t₀ X_s ds of the super process X_t with branching mechanism ψ(z)=z² and d≤3 transient Ornstein-Uhlenbeck(O.U.) underlying process, is absolutely continuous with respect to the Lebesgue measure, and its density process Y(t,x) is joint continuous in t≥0,x∈R^d.

Key words: 　ＳｕｐｅｒＯ．Ｕ．ｐｒｏｃｅｓｓ, Ｏｃｃｕｐａｔｉｏｎｔｉｍｅｐｒｏｃｅｓｓ, Ａｂｓｏｌｕｔｅｃｏｎｔｉｎｕｉｔｙ．

中图分类号:

６０Ｊ

鲍玉芳. 超Ornstein-Uhlenbeck过程的占位时过程的绝对连续性[J]. 数学物理学报, 1999, 19(1): 94-100.

Bao Yufang . The Absolution Continuity for the Occupation Time of Super Ornstein Uhlenbeck Prosces[J]. Acta mathematica scientia,Series A, 1999, 19(1): 94-100.