[کتاب][B] Stochastic calculus for fractional Brownian motion and related processes

Y Mishura - 2008‏ - books.google.com
This volume examines the theory of fractional Brownian motion and other long-memory
processes. Interesting topics for PhD students and specialists in probability theory …

[کتاب][B] Laws of small numbers: extremes and rare events

M Falk, J Hüsler, RD Reiss - 2010‏ - books.google.com
Since the publication of the first edition of this seminar book in 1994, the theory and
applications of extremes and rare events have enjoyed an enormous and still increasing …

[HTML][HTML] Extremes of Gaussian processes over an infinite horizon

AB Dieker - Stochastic processes and their applications, 2005‏ - Elsevier
Consider a centered separable Gaussian process Y with a variance function that is regularly
varying at infinity with index 2H∈(0, 2). Let φ be a 'drift'function that is strictly increasing …

Uniform tail approximation of homogenous functionals of Gaussian fields

K Dȩbicki, E Hashorva, P Liu - Advances in Applied Probability, 2017‏ - cambridge.org
Let X (t), t∈ ℝd, be a centered Gaussian random field with continuous trajectories and set ξu
(t)= X (f (u) t), t∈ ℝd, with f some positive function. Using classical results we can establish …

On the infimum attained by the reflected fractional Brownian motion

K Dębicki, KM Kosiński - Extremes, 2014‏ - Springer
Let BH (t): t≥ 0 be a fractional Brownian motion with Hurst parameter H∈(1 2, 1) H∈(12,1).
For the storage process QBH (t)= sup−∞≤ s≤ t Q_B_H(t)=\sup_-∞≤s≤t BH (t)− BH (s)− c …

An exceptional max-stable process fully parameterized by its extremal coefficients

K Strokorb, M Schlather - Bernoulli, 2015‏ - JSTOR
The extremal coefficient function (ECF) of a max-stable process X on some index set T
assigns to each finite subset A⊂ T the effective number of independent random variables …

Sojourn times of Gaussian processes with trend

K Dȩbicki, P Liu, Z Michna - Journal of Theoretical Probability, 2020‏ - Springer
We derive exact tail asymptotics of sojourn time above the level u≥ 0 P v (u)∫ 0 TI (X (t)-ct>
u) dt> x, x≥ 0, as u→∞, where X is a Gaussian process with continuous sample paths, c is …

Extremes of γ-reflected Gaussian processes with stationary increments

K Dȩbicki, E Hashorva, P Liu - ESAIM: Probability and Statistics, 2017‏ - esaim-ps.org
For a given centered Gaussian process with stationary increments X (t), t≥ 0 and c> 0, let W
γ (t)= X (t)− ct− γinf 0≤ s≤ t (X (s)− cs), t≥ 0 denote the γ-reflected process, where γ∈(0, 1) …

Stochastic differential equations driven by fractional Brownian motion and Poisson point process

L Bai, J Ma - 2015‏ - projecteuclid.org
In this paper, we study a class of stochastic differential equations with additive noise that
contains a fractional Brownian motion (fBM) and a Poisson point process of class (QL). The …

Random rewards, fractional Brownian local times and stable self-similar processes

S Cohen, G Samorodnitsky - 2006‏ - projecteuclid.org
We describe a new class of self-similar symmetric α-stable processes with stationary
increments arising as a large time scale limit in a situation where many users are earning …