Abstract:
The logarithmic asymptotic is studied for large deviation probabilities of partial sum processes based on stationary observations having a structure of the so-called moving averages of a sequence of independent identically distributed random variables. The problem is studied in the case of attraction of these processes to a fractional Brownian motion with an arbitrary Hurst parameter.
Keywords:partial sum process of moving averages, fractional Brownian motion, large deviation principle, Cameron–Martin space.