Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (2): 261-268.

• Articles • Previous Articles     Next Articles

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

 ZHONG Yu-Quan, HU Di-He   

  1. 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.

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

CLC Number: 

  • 60J99
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