Upcrossing inequalities for stationary sequences

Опубликовано 7 сентября 2016, 16:45

Let $g$ be a function which assigns to each stationary process $X_n$ and to each sample $X_1, X_2 ,..., X_n$ of the process a real number $g(X_1, ... ,X_n)$, which may also depend on the distribution of the process. I'll discuss how one can obtain effective bounds on the probability that the sequence $g(X_1, ..., X_n)$ crosses a fixed interval some number of times in terms of a quantity measuring the average