42 citations · 49 across the 9 of their papers we have counts for
9 papers
Poisson limit theorem for the number of excursions above high and medium levels by Gaussian stationary sequences
Vladimir I. Piterbarg
Asymptotic behavior of the point process of high and medium values of a Gaussian stationary process with discrete time is considered. An approximation by a Poisson cluster point pr…
High excursion probabilities for Gaussian fields on smooth manifolds
Vladimir I. Piterbarg
Gaussian random fields on finite dimensional smooth manifolds whose variances reach their maximum value at smooth submanifolds are considered. Exact asymptotic behaviors of large e…
On accompanying measures and asymptotic expansions in limit theorems for maximum of random variables
V. I. Piterbarg, Yu. A. Scherbakova
A sequence of accompanying laws is suggested in the limit theorem of B. V. Gnedenko for maximums of independent random variables belonging to maximum domain of attraction of the Gu…
Extremes of Gaussian non-stationary processes and maximal deviation of projection density estimates
Valentin Konakov, Vladimir Panov, Vladimir Piterbarg
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribut…
On maximum of Gaussian random field having unique maximum point of its variance
Sergey G. Kobelkov, Vladimir I. Piterbarg
Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute…
On maximum of Gaussian process with unique maximum point of its variance
E. Hashorva, S. Kobelkov, V. I. Piterbarg
Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of the…
Stochastic representation and pathwise properties of fractional Cox-Ingersoll-Ross process
Yuliya Mishura, Vladimir I. Piterbarg, Kostiantyn Ralchenko +1
We consider the fractional Cox-Ingersoll-Ross process satisfying the stochastic differential equation (SDE) driven by a fractional Brownian…
Asymptotic Expansion of Gaussian Chaos via Probabilistic Approach
Enkelejd Hashorva, Dmitry Korshunov, Vladimir I. Piterbarg
For a centered -dimensional Gaussian random vector and a homogeneous function we derive asymptotic expansions for the tail of the Gaussian chao…
On the Supremum of gamma-reflected Processes with Fractional Brownian Motion as Input
Enkelejd Hashorva, Lanpeng Ji, Vladimir I. Piterbarg
Let be a fractional Brownian motion with Hurst index $H\in(0,1}$ and define a gamma-reflected process $W_\Ga(t)=X_H(t)-ct-\gammainf_{s\in[0,t]}\left(X_H(s)-cs \rig…