| 1. |
- Albin, Patrik, 1960
(author)
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ON EXTREME VALUE THEORY FOR GROUP STATIONARY GAUSSIAN PROCESSES
- 2018
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In: Esaim-Probability and Statistics. - : EDP Sciences. - 1292-8100 .- 1262-3318. ; 22, s. 1-18
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Journal article (peer-reviewed)abstract
- We study extreme value theory of right stationary Gaussian processes with parameters in open subsets with compact closure of (not necessarily Abelian) locally compact topological groups. Even when specialized to Euclidian space our result extend results on extremes of stationary Gaussian processes and fields in the literature by means of requiring weaker technical conditions as well as by means of the fact that group stationary processes need not be stationary in the usual sense (that is, with respect to addition as group operation).
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| 2. |
- Albin, Patrik, 1960, et al.
(author)
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Extremes and limit theorems for difference of chi-type processes
- 2016
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In: ESAIM - Probability and Statistics. - : EDP Sciences. - 1262-3318 .- 1292-8100. ; 20, s. 349-366
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Journal article (peer-reviewed)abstract
- © 2016 EDP Sciences, SMAI. Let { m,k (k) (t),t≥ 0},κ > 0 be random processes defined as the differences of two independent stationary chi-type processes with m and k degrees of freedom. In this paper we derive the asymptotics of P supt [0,T[ m,k (k) (t) > u →∞, u→∞ under some assumptions on the covariance structures of the underlying Gaussian processes. Further, we establish a Berman sojourn limit theorem and a Gumbel limit result.
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| 3. |
- Albin, Patrik, 1960, et al.
(author)
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On the Asymptotic Behaviour of Superexponential Lévy Processes
- 2023
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In: Esaim-Probability and Statistics. - 1292-8100 .- 1262-3318. ; 27, s. 810-840
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Journal article (peer-reviewed)abstract
- We study tail probabilities of superexponential infinite divisible distributions as well as tail probabilities of suprema of Levy processes with superexponential marginal distributions over compact intervals.
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| 4. |
- Albin, Patrik, 1960
(author)
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On covariance functions with slowly or regularly varying modulo of continuity
- 2018
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In: Statistics and Probability Letters. - : Elsevier BV. - 0167-7152. ; 138, s. 177-182
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Journal article (peer-reviewed)abstract
- By means of Fourier transforms we show that more or less any regularly varying or slowly varying function can feature as the modulo of continuity in squared mean sense of a stationary stochastic process.
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| 5. |
- Albin, Patrik, 1960
(author)
-
A continuous non-Brownian motion martingale with Brownian motion marginal distributions
- 2008
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In: Statistics and Probability Letters. - 0167-7152. ; 78:6, s. 682-686
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Journal article (peer-reviewed)abstract
- This note exhibits a continuous martingale $M$ which is not Brownian motion, but has the same univariate marginal distributions as Brownian motion. It is given by $M(t)=X_1(t)X_2(t)Y$, where $X_1$ and $X_2$ are independent copies of the diffusion $dX(t)=dB(t)(2X(t))^{-1},\ X(0)=0$, and $Y$ is an independent random variable with known density on $(0,\sqrt{2})$. The existence of such a martingale was an open problem until now.
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| 6. |
- Albin, Patrik, 1960, et al.
(author)
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A New Proof of an Old Result by Pickands
- 2010
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In: Electronic Communications in Probability. - 1083-589X. ; 15, s. 339-345
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Journal article (peer-reviewed)abstract
- Let {xi(t)}(t is an element of[0,h]) be a stationary Gaussian process with covariance function r such that r(t) = 1 - C vertical bar t vertical bar(alpha) + o(vertical bar t vertical bar(alpha)) as t -> 0. We give a new and direct proof of a result originally obtained by Pickands, on the asymptotic behaviour as u -> infinity of the probability P{sup(t is an element of vertical bar 0,h vertical bar) xi(t) > u} that the process xi exceeds the level u. As a by-product, we obtain a new expression for Pickands constant H alpha
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