2 Citations
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,…
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…
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…
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…
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…
Adventures in stochastic processes
- Mathematics
- 1992
Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many…
Lévy processes : theory and applications
- Mathematics
- 2001
Preface I. A tutorial on Levy processes Sato, K.: Basic results on Levy processes II. Distributional, pathwise and structural results Carmona, P. / Petit, F. / Yor, M.: Exponentials functionals of…
Stochastic Processes and their Applications
- Philosophy
- 2006
Well, someone can decide by themselves what they want to do and need to do but sometimes, that kind of person will need some stochastic processes and their applications references. People with open…