2 Citations
Regularly varying functions
- Mathematics
- 2006
We consider some elementary functions of the components of a regularly varying random vector such as linear combinations, products, min- ima, maxima, order statistics, powers. We give conditions…
A landscape of peaks: The intermittency islands of the stochastic heat equation with L\'evy noise
- Mathematics
- 2022
We show that the spatial profile of the solution to the stochastic heat equation features multiple layers of intermittency islands if the driving noise is non-Gaussian. On the one hand, as expected,…
References
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Extremal behavior of stochastic integrals driven by regularly varying Levy processes
- Mathematics
- 2005
We study the extremal behavior of a stochastic integral driven by a multivariate Levy process that is regularly varying with index alpha > 0. For predictable integrands with a finite (alpha +…
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
- Mathematics
- 1995
Stable random variables on the real line Multivariate stable distributions Stable stochastic integrals Dependence structures of multivariate stable distributions Non-linear regression Complex stable…
Extremes of stochastic volatility models
- Mathematics
- 1998
We consider extreme value theory for stochastic volatility processes in both cases of light-tailed and heavy-tailed noise. First, the asymptotic behavior of the tails of the marginal distribution is…
Extremes of Moving Averages of Random Variables with Finite Endpoint
- Mathematics
- 1991
where {Zj) are iid and nonnegative random variables and c; > 0 are constants satisfying summability conditions at least sufficient to make the random series above converge. We suppose that the…
Series Representations of Lévy Processes from the Perspective of Point Processes
- Mathematics
- 2001
Several methods of generating series representations of a Levy process are presented under a unified approach and a new rejection method is introduced in this context. The connection of such…
On a strong Tauberian result
- Mathematics
- 1983
SummaryWe consider the determination of the behavior of a distribution function F at its endpoints in terms of the behavior of its Laplace-Stieltjes transform Ω at the limits of its interval of…
Stochastic integration and differential equations
- Mathematics
- 1990
I Preliminaries.- II Semimartingales and Stochastic Integrals.- III Semimartingales and Decomposable Processes.- IV General Stochastic Integration and Local Times.- V Stochastic Differential…
Regular Variation in R k
- Mathematics
- 1988
Researchers investigating certain limit theorems in probability have discovered a multivariable analogue to Karamata's theory of regularly varying functions. The method uses elements of real analysis…
One-dimensional stable distributions
- Mathematics
- 1986
Examples of stable laws in applications Analytic properties of the distributions in the family $\mathfrak S$ Special properties of laws in the class $\mathfrak W$ Estimators of the parameters of…