ON INFINITE SERIES OF INDEPENDENT ORNSTEIN-UHLENBECK PROCESSES

[摘要] We establish moduli of continuity and large increment properties for stationary increment Gaussian processes in order to study the path behavior of infinite series of independent Ornstein-Uhlenbeck processes. The existence and continuity of the latter infinite series type Gaussian processes are proved via showing that under a global condition their partial sum processes converge uniformly over finite intervals with probability one.

[发布日期] 1991-10-01

[关键词] INFINITE DIMENSIONAL ORNSTEIN-UHLENBECK PROCESSES;STATIONARY INCREMENT GAUSSIAN PROCESS;SAMPLE PATH PROPERTIES