On the uniqueness of maximizers of Markov–Gaussian processes

Abstract

Abstract Let Y be a nonconstant Markov–Gaussian process with almost sure continuous sample functions. We show that with probability one the original process Y and the reflected process |Y| in each case attain their maximal value at precisely one point. Almost sure uniqueness of maximizers of stochastic processes plays an important role when deriving the limit distribution of M-estimators.