Existence and Joint Continuity of Local Time of Multiparameter Fractional Léy Processes
-
摘要: 首先引进了一类比Xiao和Zhang研究过的Gauss随机场更为一般的多参数Lévy过程.然后给出并证明了此过程的一种分解,并利用这一分解,证明了该过程的局部时的存在性和联合连续性.
-
关键词:
- 多参数分数Lévy过程 /
- 分数Brown单 /
- 局部时 /
- Gauss随机场 /
- 多参数Poisson过程 /
- 多参数Brown运动
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. -
[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. Hlder 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
计量
- 文章访问数: 2416
- HTML全文浏览量: 85
- PDF下载量: 669
- 被引次数: 0