Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (5): 1155-1164.doi: 10.1016/S0252-9602(09)60093-X

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LOCAL TIME ANALYSIS OF ADDITIVE L\'EVY PROCESSES WITH DIFFERENT LÉVY EXPONENTS

 ZHONG Yu-Quan   

  1. School of Computer, Panzhihua University, Panzhihua 617000, China
  • Received:2008-02-04 Online:2009-09-20 Published:2009-09-20

Abstract:

Let X1,…,XN be independent, classical Lévy processes on Rd with Lévy exponents Ψ1,…,ΨN, respectively. The
corresponding  additive Lévy process is defined as the following $N$-parameter random field on Rd, X(t)=X1(t1)+…+XN(tN), ∨t ∈ RN+. Under mild regularity conditions on the Ψi's, we derive estimate for the local and uniform moduli of continuity of local times of X={X(t);t ∈ RN+}.

Key words: additive Lévy pocesses, local time, Hölder laws

CLC Number: 

  • 60G52
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