On the uniqueness of maximizers of Markov–Gaussian processes

✍ Scribed by Dietmar Ferger

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 92 KB
• Volume: 45
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00044-9

✦ Synopsis

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 re ected 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.