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Ruin probability for Gaussian integrated processes
- K. Dȩbicki
- 1 March 2002
A note on LDP for supremum of Gaussian processes over infinite horizon
- K. Dȩbicki
- 15 September 1999
Exact overflow asymptotics for queues with many Gaussian inputs
This paper considers a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments and considers both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon.
Open problems in Gaussian fluid queueing theory
This work addresses the problem of characterizing the correlation structure of the stationary buffer content process, the speed of convergence to stationarity, and analysis of an asymptotic constant associated with the stationarybuffer content distribution (the so-called Pickands constant).
Asymptotics of supremum distribution of α(t)-locally stationary Gaussian processes
Queues and Lévy fluctuation theory
The book provides an extensive introduction to queueing models driven by Levy-processes as well as a systematic account of the literature on Levy-driven queues. The objective is to make the reader…
Parisian ruin over a finite-time horizon
For a risk process Ru(t) = u + ct − X(t), t ≥ 0, where u ≥ 0 is the initial capital, c > 0 is the premium rate and X(t), t ≥ 0 is an aggregate claim process, we investigate the probability of the…
A note on upper estimates for Pickands constants
Parisian ruin of self-similar Gaussian risk processes
The exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes are derived and an asymPTotic relation between the Parisian and the classical ruin times is derived.