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.
- infinite dimensional Ornstein-Uhlenbeck processes
- sample path properties
- stationary increment Gaussian process
ASJC Scopus subject areas
- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics