SELF-INTERSECTION LOCAL TIME OF ADDITIVE L´|EVY PROCESS

数学物理学报(英文版) ›› 2002, Vol. 22 ›› Issue (2): 261-268.

SELF-INTERSECTION LOCAL TIME OF ADDITIVE L´|EVY PROCESS

钟玉泉, 胡迪鹤

Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China Department of Base, Panzhihua University, Panzhihua 617000, China Department of Mathematics, Wuhan University, Wuhan 430072, China

出版日期:2002-04-15 发布日期:2002-04-15
基金资助:
Supported by the National Natural Science Foundation and the Doctoral ProgrammeFoundation of China.

SELF-INTERSECTION LOCAL TIME OF ADDITIVE L´|EVY PROCESS

ZHONG Yu-Quan, HU Di-He

Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China Department of Base, Panzhihua University, Panzhihua 617000, China Department of Mathematics, Wuhan University, Wuhan 430072, China

Online:2002-04-15 Published:2002-04-15
Supported by:
Supported by the National Natural Science Foundation and the Doctoral ProgrammeFoundation of China.

摘要/Abstract

摘要：

This article discusses the problem of existence of jointly continuous self-intersection local time for an additive l´evy process. Here, ”local time” is understood in the sense of occupation density, and by an additive L´evy process the authors mean a process X = {X(t), t 2 RN+)} which has the decomposition X = X1 X2 · · ·XN, each X? has the lower index ?, = min{1, · · · , N}. Let Z = (Xt2 − Xt1 , · · · ,Xtr − Xtr−1 ).
They prove that if Nr > d(r − 1), then a jointly continuous local time of Z, i.e. the self-intersection local time of X, can be obtained.

关键词: Additive Le´vy process, local time, self-intersection local time, Le´vy process,isotropic stable process

Abstract:

This article discusses the problem of existence of jointly continuous self-intersection local time for an additive l´evy process. Here, ”local time” is understood in the sense of occupation density, and by an additive L´evy process the authors mean a process X = {X(t), t 2 RN+)} which has the decomposition X = X1 X2 · · ·XN, each X? has the lower index ?, = min{ 1, · · · , N}. Let Z = (Xt2 − Xt1 , · · · ,Xtr − Xtr−1 ).
They prove that if Nr > d(r − 1), then a jointly continuous local time of Z, i.e. the self-intersection local time of X, can be obtained.

Key words: Additive Le´vy process, local time, self-intersection local time, Le´vy process,isotropic stable process

中图分类号:

60J99

钟玉泉, 胡迪鹤. SELF-INTERSECTION LOCAL TIME OF ADDITIVE L´|EVY PROCESS[J]. 数学物理学报(英文版), 2002, 22(2): 261-268.

ZHONG Yu-Quan, HU Di-He. SELF-INTERSECTION LOCAL TIME OF ADDITIVE L´|EVY PROCESS[J]. Acta mathematica scientia,Series B, 2002, 22(2): 261-268.

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SELF-INTERSECTION LOCAL TIME OF ADDITIVE L´|EVY PROCESS

SELF-INTERSECTION LOCAL TIME OF ADDITIVE L´|EVY PROCESS

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