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The Annals of probability, ISSN 0091-1798, 2009, Volume 37, Issue 5, pp. 2042 - 2065
Journal Article
Journal of theoretical probability, ISSN 1572-9230, 2019
We derive exact tail asymptotics of sojourn time above the level $u\geq 0$ $$ \mathbb{P}\left(v(u)\int_0^T \mathbb{I}(X(t)-ct>u)d t>x\right), \quad x\geq 0 $$... 
Mathematics - Probability
Journal Article
The Annals of applied probability, ISSN 1050-5164, 2/2003, Volume 13, Issue 1, pp. 37 - 53
We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We... 
Integers | Logical proofs | Random walk | Stochastic processes | Random variables | Indicator functions | Stopping distances | Distribution functions | Ruin probability | Long-tailed distribution | Subexponential distribution | DISTRIBUTIONS | STATISTICS & PROBABILITY | ruin probability | long-tailed distribution | subexponential distribution | 60K30 | 60G70 | 60K25
Journal Article
Journal of applied probability, ISSN 0021-9002, 06/2007, Volume 44, Issue 2, pp. 428 - 443
We provide a distributional study of the solution to the classical control problem due to De Finetti (1957), Gerber (1969), Azcue and Muler (2005), and Avram... 
Insurance risk process | Reflected Lévy process | Integrated exponential Lévy process | Passage problem | Ruin | insurance risk process | 60K05 | 60G70 | passage problem | 60K15 | ruin | 91B30 | integrated exponential Lévy process | 60J55
Journal Article
The Annals of statistics, ISSN 0090-5364, 4/2015, Volume 43, Issue 2, pp. 903 - 934
The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the... 
Bias correction | Threshold choice | Tail dependence | Multivariate extreme value theory | PROBABILITY | bias correction | MODELS | STATISTICS | ESTIMATORS | STATISTICS & PROBABILITY | INDEX | tail dependence | PICKANDS DEPENDENCE | threshold choice | Statistics | Statistics Theory | Mathematics | 62G05 | 62G20 | 60G70 | 62G32 | 60F05
Journal Article
Journal of applied probability, ISSN 0021-9002, 03/2015, Volume 52, Issue 1, pp. 68 - 81
Let W = { W n : n ∈ N} be a sequence of random vectors in R d , d ≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of W , that is,... 
Large deviation theory | Extrema of stochastic process | 60G70 | 60F10 | large deviation theory
Journal Article
Journal of applied probability, ISSN 0021-9002, 09/2014, Volume 51, Issue 3, pp. 713 - 726
Define a γ-reflected process W γ(t) = Y H (t) - γinf s∈[0,t] Y H (s), t ≥ 0, with input process {Y H (t), t ≥ 0}, which is a fractional Brownian motion with... 
Passage time | Piterbarg constant | γ-reflected process | Risk process with tax | Workload process | Fractional Brownian motion | Pickands constant | Gaussian approximation | workload process | 60G70 | fractional Brownian motion | passage time | risk process with tax | 60G15
Journal Article
Advances in applied probability, ISSN 0001-8678, 03/2013, Volume 45, Issue 1, pp. 186 - 213
An asymptotic model for the extreme behavior of certain Markov chains is the ‘tail chain’. Generally taking the form of a multiplicative random walk, it is... 
General Applied Probability | Markov chain | Transition kernel | Tail chain | Multivariate regular variation | Heavy tail | Extreme values | tail chain | heavy tail | multivariate regular variation | 60G70 | 62P05 | 60J05 | transition kernel
Journal Article
Journal Article
Journal of applied probability, ISSN 0021-9002, 12/2012, Volume 49, Issue 4, pp. 1106 - 1118
Let {X n (t), t∈[0,∞)}, n∈ℕ, be standard stationary Gaussian processes. The limit distribution of t∈[0,T(n)]|X n (t)| is established as r n (t), the... 
Stationary Gaussian process | Pickands' constant | Strong dependence | Berman's condition | Limit theorem | Mathematics - Probability | strong dependence | 60G70 | limit theorem | 60G15
Journal Article
The Annals of applied probability, ISSN 1050-5164, 8/2008, Volume 18, Issue 4, pp. 1351 - 1378
Journal Article
Advances in applied probability, ISSN 0001-8678, 03/2013, Volume 45, Issue 1, pp. 139 - 163
Multivariate regular variation plays a role in assessing tail risk in diverse applications such as finance, telecommunications, insurance, and environmental... 
General Applied Probability | Risk set | Spectral measure | Vague Convergence | Asymptotic independence | Regular variation | 60F99 | risk set | 60G70 | 62G32 | vague convergence | regular variation | spectral measure | asymptotic independence
Journal Article
Advances in applied probability, ISSN 0001-8678, 12/2012, Volume 44, Issue 4, pp. 1142 - 1172
Let {X i} be a sequence of independent, identically distributed random variables with an intermediate regularly varying right tail F̄. Let (N, C 1, C 2,…) be a... 
General Applied Probability | Randomly weighted sum | Intermediate regular variation | Regular variation | Heavy tail | Breiman's theorem | Randomly stopped sum | heavy tail | 60F10 | 60G50 | 60J80 | randomly stopped sum | 60G70 | intermediate regular variation | regular variation
Journal Article
Journal Article
Journal of applied probability, ISSN 0021-9002, 09/2015, Volume 52, Issue 3, pp. 688 - 702
In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal... 
Research Papers | normal approximation | generalized Pickands' constant | Parisian ruin time | 60G70 | Parisian ruin probability | fractional Brownian motion | self-similar Gaussian process | 60G15
Journal Article
The Annals of probability, ISSN 0091-1798, 5/2012, Volume 40, Issue 3, pp. 1069 - 1104
This paper develops asymptotic approximations of P(∫ T e f(t) dt > b) as b → ∞ for a homogeneous smooth Gaussian random field, f, living on a compact... 
Approximation | Covariance | Mathematical integrals | Logical proofs | Log integral function | Eigenvalues | Finite sums | Jordan matrices | Matrices | Random variables | Extremes | Gaussian random field | BROWNIAN-MOTION | COUNTS | MAXIMUM | VALUE-AT-RISK | INEQUALITY | TIME-SERIES | STATISTICS & PROBABILITY | REGRESSION-MODEL | extremes | RANDOM-VARIABLES | SUMS | Mathematics - Probability | 60G70 | 60F10
Journal Article
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