Existence and Joint Continuity of Local Time of Multiparameter Fractional Léy Processes

LIN Zheng-yan; CHENG Zong-mao

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LIN Zheng-yan, CHENG Zong-mao. Existence and Joint Continuity of Local Time of Multiparameter Fractional Léy Processes[J]. Applied Mathematics and Mechanics, 2009, 30(3): 360-368.

Citation:

LIN Zheng-yan, CHENG Zong-mao. Existence and Joint Continuity of Local Time of Multiparameter Fractional Léy Processes[J]. Applied Mathematics and Mechanics, 2009, 30(3): 360-368.

Citation:

LIN Zheng-yan, CHENG Zong-mao. Existence and Joint Continuity of Local Time of Multiparameter Fractional Léy Processes[J]. Applied Mathematics and Mechanics, 2009, 30(3): 360-368.

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Existence and Joint Continuity of Local Time of Multiparameter Fractional Léy Processes

LIN Zheng-yan¹,
CHENG Zong-mao^1,2

1.
Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China;

Received Date: 2008-06-30
Rev Recd Date: 2008-12-01
Publish Date: 2009-03-15

Abstract

Abstract

The definition of multiparameter fractional Lvy process which more general than that studied by Xiao and Zhang was introduced firstly, and then a decomposition for it was given and shown. Later using this decomposition, existence and joint continuity of its local time were proved.
- multipar ameter fractional Lvy process,
- fractional Brownian sheet,
- local time,
- Gaussian random field,
- multiparameter Poisson process,
- multiparameter Brownian motion

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References(12)

References

[1]	Orey S,Pruitt W E.Sample functions of the N-parameter Wiener process[J].Ann Probab,1973,1(1):138-163. doi: 10.1214/aop/1176997030
[2]	Adler R J. The uniform dimension of the level sets of a Brownian sheet[J].Ann Probab,1978,6(2):509-515. doi: 10.1214/aop/1176995535
[3]	Adler R J. The Geometry of Random Fields[M].New York:Wiley,1981.
[4]	Pitt L D.Local times for Gaussian vector fields[J].Indiana Univ Math J,1978,27(3):309-330. doi: 10.1512/iumj.1978.27.27024
[5]	Ehm W.Sample function properties of multi-parameter stable processes[J].Z Wahrsch Verw Gebiete,1981,56(2):195-228. doi: 10.1007/BF00535741
[6]	Rosen J.Self-intersections of random fields[J].Ann Probab,1984,12(1):108-119. doi: 10.1214/aop/1176993376
[7]	Talagrand M.Hausdorff measure of trajectories of multiparameter fractional Brownian[J].Ann Probab,1995,23(4):767-775. doi: 10.1214/aop/1176988288
[8]	Xiao Y. Hlder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields[J].Probab Theory Reated Fields,1997,109(1):129-157. doi: 10.1007/s004400050128
[9]	Xiao Y,Zhang T.Local times of fractional Brownian sheets probab[J].Th Ret Fields,2002,124(2):204-226. doi: 10.1007/s004400200210
[10]	Geman D,Horowitz J.Occupation densities[J].Ann Probab,1980,8(1):1-67. doi: 10.1214/aop/1176994824
[11]	Bertoin J.Lévy Processes[M].London:Cambridge Press,1996.
[12]	Geman D,Horowitz J,Rosen J.A local time analysis of intersections of Brownian paths in the plane[J].Ann Probab,1984,12(1):86-107. doi: 10.1214/aop/1176993375