| 1. |
- Albin, Patrik, 1960, et al.
(författare)
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Extremes and limit theorems for difference of chi-type processes
- 2016
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Ingår i: ESAIM - Probability and Statistics. - : EDP Sciences. - 1262-3318 .- 1292-8100. ; 20, s. 349-366
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Tidskriftsartikel (refereegranskat)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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| 2. |
- Albin, Patrik, 1960
(författare)
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ON EXTREME VALUE THEORY FOR GROUP STATIONARY GAUSSIAN PROCESSES
- 2018
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Ingår i: Esaim-Probability and Statistics. - : EDP Sciences. - 1292-8100 .- 1262-3318. ; 22, s. 1-18
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Tidskriftsartikel (refereegranskat)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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| 3. |
- Albin, Patrik, 1960, et al.
(författare)
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On the Asymptotic Behaviour of Superexponential Lévy Processes
- 2023
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Ingår i: Esaim-Probability and Statistics. - 1292-8100 .- 1262-3318. ; 27, s. 810-840
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Tidskriftsartikel (refereegranskat)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. |
- Dombry, Clement, et al.
(författare)
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Moment measures of heavy-tailed renewal point processes : asymptotics and applications
- 2013
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Ingår i: ESAIM. P&S. - : EDP Sciences. - 1292-8100 .- 1262-3318. ; 17, s. 567-591
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Tidskriftsartikel (refereegranskat)abstract
- We study higher-order moment measures of heavy-tailed renewal models, including a renewal point process with heavy-tailed inter-renewal distribution and its continuous analog, the occupation measure of a heavy-tailed Lévy subordinator. Our results reveal that the asymptotic structure of such moment measures are given by explicit power-law density functions. The same power-law densities appear naturally as cumulant measures of certain Poisson and Gaussian stochastic integrals. This correspondence provides new and extended results regarding the asymptotic fluctuations of heavy-tailed sources under aggregation, and clarifies existing links between renewal models and fractional random processes.
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| 5. |
- Ekström, Erik, et al.
(författare)
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Bayesian sequential composite hypothesis testing in discrete time
- 2022
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Ingår i: ESAIM. P&S. - : EDP Sciences. - 1292-8100 .- 1262-3318. ; 26, s. 265-282
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Tidskriftsartikel (refereegranskat)abstract
- We study the sequential testing problem of two alternative hypotheses regarding an unknown parameter in an exponential family when observations are costly. In a Bayesian setting, the problem can be embedded in a Markovian framework. Using the conditional probability of one of the hypotheses as the underlying spatial variable, we show that the cost function is concave and that the posterior distribution becomes more concentrated as time goes on. Moreover, we study time monotonicity of the value function. For a large class of model specifications, the cost function is non-decreasing in time, and the optimal stopping boundaries are thus monotone.
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| 6. |
- Ekström, Erik, et al.
(författare)
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Bayesian Sequential Testing Of The Drift Of A Brownian Motion
- 2015
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Ingår i: ESAIM. P&S. - : EDP Sciences. - 1292-8100 .- 1262-3318. ; 19, s. 626-648
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Tidskriftsartikel (refereegranskat)abstract
- We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the 0-1 loss function and a constant cost of observation per unit of time for general prior distributions. The statistical problem is reformulated as an optimal stopping problem with the current conditional probability that the drift is non-negative as the underlying process. The volatility of this conditional probability process is shown to be non-increasing in time, which enables us to prove monotonicity and continuity of the optimal stopping boundaries as well as to characterize them completely in the finite-horizon case as the unique continuous solution to a pair of integral equations. In the infinite-horizon case, the boundaries are shown to solve another pair of integral equations and a convergent approximation scheme for the boundaries is provided. Also, we describe the dependence between the prior distribution and the long-term asymptotic behaviour of the boundaries.
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| 7. |
- Gugushvili, S., et al.
(författare)
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Bayesian wavelet de-noising with the caravan prior
- 2020
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Ingår i: Esaim-Probability and Statistics. - : EDP Sciences. - 1292-8100 .- 1262-3318. ; 23, s. 947-978
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Tidskriftsartikel (refereegranskat)abstract
- According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising approach that takes into account such a feature of the signal may in practice outperform other, more vanilla methods, both in terms of the estimation error and visual appearance of the estimates. Motivated by this observation, we present a Bayesian approach to wavelet de-noising, where dependencies between neighbouring wavelet coefficients are a priori modelled via a Markov chain-based prior, that we term the caravan prior. Posterior computations in our method are performed via the Gibbs sampler. Using representative synthetic and real data examples, we conduct a detailed comparison of our approach with a benchmark empirical Bayes de-noising method (due to Johnstone and Silverman). We show that the caravan prior fares well and is therefore a useful addition to the wavelet de-noising toolbox.
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| 8. |
- Lifshits, Mikhail, et al.
(författare)
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Bifractional Brownian motion: existence and border cases
- 2015
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Ingår i: ESAIM. P&S. - : EDP Sciences. - 1292-8100 .- 1262-3318. ; 19:766
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Tidskriftsartikel (refereegranskat)abstract
- Bifractional Brownian motion (bfBm) is a centered Gaussian process with covariance R(H,K)(s,t) = 2−K((|s|2H + |t|2H)K − |t − s|2HK), s,t ∈ ℝWe study the existence of bfBm for a given pair of parameters (h,k) and encounter some related limiting processes.
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| 9. |
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