Extremes of Stationary Processes

Abstract

Consider a stationary real-valued process (X _n; n≥1) or (X_t; t≥0). Time may be discrete or continuous; the marginal distribution may be discrete or continuous; the process may or may not be Markov. Let

$$ {M_n} = \mathop {\max }\limits_{1 \leqslant j \leqslant n} {X_j};{M_t} = \mathop {\sup }\limits_{0 \leqslant s \leqslant t} {X_s} $$