Asymptotic Maxima of Continuous Gaussian Processes

Expected Number of Local Maxima of Some Gaussian Random Polnomials

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Week 3 Continuous time Gaussian processes

This week we take the limit ∆t → 0. The limit is a process Xt that is defined for all t in some range, such as t ∈ [0, T ]. The process takes place in continuous time. This week, Xt is a continuous function of t. The process has continuous sample paths. It is natural to suppose that the limit of a Markov process is a continuous time Markov process. The limits we obtain this week will be either ...

Asymptotic Distribution for the Sum and Maximum of Gaussian Processes

Previous work on the joint asymptotic distribution of the sum and maxima of Gaussian processes is extended here. In particular, it is shown that for a stationary sequence of standard normal random variables with correlation function r, the condition r(n) log n = o(1) as n →∞ suffices to establish the asymptotic independence of the sum and maximum.

An Asymptotic Property of Gaussian Processes . K 1 )