Functional limit theorems for the infinite series of OU processes in Hölder norm

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Abstract

In this paper, estimating large deviation probabilities for the infinite series of independent OU processes in Hölder norm, we obtain functional limit theorems for this process in the Hölder norm, which include functional modulus of continuity and functional LIL for the infinite series of independent OU processes in the Hölder norm.

Keywords

Ornstein–Uhlenbeck process
Stationary Gaussian process
Functional limit theorem
Functional law of the iterated logarithm
Functional modulus of continuity
Large deviation probability

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