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Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
Stable random variables on the real line Multivariate stable distributions Stable stochastic integrals Dependence structures of multivariate stable distributions Non-linear regression Complex stable
Long Range Dependence
The notion of long range dependence is discussed from a variety of points of view, and a new approach is suggested, including connections with non-stationary processes.
Extreme Value Theory as a Risk Management Tool
The financial industry, including banking and insurance, is undergoing major changes. The (re)insurance industry is increasingly exposed to catastrophic losses for which the requested cover is only
The supremum of a negative drift random walk with dependent heavy-tailed steps
Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum
Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes
We study the partial maxima of stationary α-stable processes. We relate their asymptotic behavior to the ergodic theoretical properties of the flow. We observe a sharp change in the asymptotic
Functional large deviations for multivariate regularly varying random walks
We extend classical results by A. V. Nagaev [Izv Akad. Nauk UzSSR Ser Fiz.-Mat. Nauk 6 (1969) 17-22, Theory Probab. Appl. 14 (1969) 51-64, 193-208] on large deviations for sums of i.i.d. regularly
Tail probabilities for infinite series of regularly varying random vectors
A random vector X with representation X = Sigma(j >= 0)A(j)Z(j) is considered. Here, (Z(j)) is a sequence of independent and identically distributed random vectors and (A(j)) is a sequence of random
Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models
On/off models are common inputs for a variety of communication network models as well as storage and inventory models and have dramatic consequences for fluid models where fluid flows in at constant rate and there is a constant rate of release.