Zhongquan Tan

Asymptotics of maxima of strongly dependent Gaussian processes

Let

Piterbarg's max-discretization theorem for stationary vector Gaussian processes observed on different grids

\{X_{n}(t), t\in[0,\infty)\}, n\in\mathbb{N}

Large deviations of Shepp statistics for fractional Brownian motion

be a sequence of centered dependent stationary Gaussian processes. The limit distribution of

On maxima of chi-processes over threshold dependent grids

\sup_{t\in[0,T(n)]}|X_{n}(t)|

Exact asymptotics and limit theorems for supremum of stationary χ-processes over a random interval

is established as

Limit theorems for extremes of strongly dependent cyclo-stationary χ-processes

r_{n}(t)

On Piterbarg Max-Discretisation Theorem for Standardised Maximum of Stationary Gaussian Processes

, the correlation function of

Exact tail asymptotics of the supremum of strongly dependent Gaussian processes over a random interval

X_{n}

On Piterbarg’s max-discretisation theorem for multivariate stationary Gaussian processes

satisfies the local and long range strong dependence conditions, which extends the results obtained by Seleznjev (1991).

On the infinite sums of deflated Gaussian products

In this paper, we derive Piterbargs max-discretization theorem for two different grids considering centred stationary vector Gaussian processes. So far in the literature results in this direction have been derived for the joint distribution of the maximum of Gaussian processes over and over a grid . In this paper, we extend the recent findings by considering additionally the maximum over another grid . We derive the joint limiting distribution of maximum of stationary Gaussian vector processes for different choices of such grids by letting . As a by-product we find that the joint limiting distribution of the maximum over different grids, which we refer to as the Piterbarg distribution, is in the case of weakly dependent Gaussian processes a max-stable distribution.