V. I. Piterbarg
YOU?
Author Swipe
View article: Poisson limit theorem for the number of excursions above high and medium levels by Gaussian stationary sequences
Poisson limit theorem for the number of excursions above high and medium levels by Gaussian stationary sequences Open
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 process is given for the point process.
View article: High excursion probabilities for Gaussian fields on smooth manifolds
High excursion probabilities for Gaussian fields on smooth manifolds Open
Gaussian random fields on finite dimensional smooth manifolds whose variances reach their maximum value at smooth submanifolds are considered. Exact asymptotic behaviors of large excursion probabilities have been evaluated. Vector Gaussian…
View article: On accompanying measures and asymptotic expansions in limit theorems for maximum of random variables
On accompanying measures and asymptotic expansions in limit theorems for maximum of random variables Open
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 Gumbel distribution. It is shown that this sequence gives an …
View article: Extremes of Gaussian non-stationary processes and maximal deviation of projection density estimates
Extremes of Gaussian non-stationary processes and maximal deviation of projection density estimates Open
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 distribution. Unlike previously known facts in this field, our main …
View article: High excursions of Bessel process and other processes of Bessel type
High excursions of Bessel process and other processes of Bessel type Open
A high excursion probability for the modulus of a Gaussian vector process with independent identically distributed components is evaluated. It is assumed that the components have means zero and variances reaching its absolute maximum at a …
View article: On maximum of Gaussian random field having unique maximum point of its\n variance
On maximum of Gaussian random field having unique maximum point of its\n variance Open
Gaussian random fields on Euclidean spaces whose variances reach their\nmaximum values at unique points are considered. Exact asymptotic behaviors of\nprobabilities of large absolute maximum of theirs trajectories have been\nevaluated usin…
View article: Stochastic representation and path properties of a fractional Cox–Ingersoll–Ross process
Stochastic representation and path properties of a fractional Cox–Ingersoll–Ross process Open
We consider the Cox–Ingersoll–Ross process that satisfies the stochastic differential equation $dX_t = aX_t dt+\sigma \sqrt {X_t} dB^H_t$ driven by a fractional Brownian motion $B^H_t$ with the Hurst index exceeding $\frac {2}{3}$, where $…
View article: On maximum of Gaussian process with unique maximum point of its variance
On maximum of Gaussian process with unique maximum point of its variance Open
Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Metho…
View article: Stochastic representation and pathwise properties of fractional Cox-Ingersoll-Ross process
Stochastic representation and pathwise properties of fractional Cox-Ingersoll-Ross process Open
We consider the fractional Cox-Ingersoll-Ross process satisfying the stochastic differential equation (SDE) $dX_t = aX_t\,dt + σ\sqrt{X_t}\,dB^H_t$ driven by a fractional Brownian motion (fBm) with Hurst parameter exceeding $\frac{2}{3}$. …