LARGE DEVIATIONS FOR SELF INTERSECTION LOCAL TIMES OF ORNSTEIN-UHLENBECK PROCESSES

In the area of large deviations, people concern about the asymptotic computation of small probabilities on an exponential scale. The general form of large deviations can be roughly described as: P{Yn ∈ A} ≈ exp{−bnI(A)} (n → ∞), for a random sequence {Yn}, a positive sequence bn with bn → ∞, and a coefficient I(A) ≥ 0. In applications, we often concern about the probability that the random variables take large values, that is we concern about the P{Yn ≥ λ}, where λ > 0. Here, we consider the Ornstein-Uhlenbeck process, study the properties of the local times and self intersection local times of that process, and focus on the large deviations for the self intersection local times of the Ornstein-Uhlenbeck process. A function that we need to study and plays an important role in large deviations is called logarithmic moment generating function.