Rare event analysis and efficient simulation for a multidimensional ruin problem
| Autor: | Bert Zwart, Ewan Jacov Cahen, Michel Mandjes |
|---|---|
| Přispěvatelé: | Stochastics (KDV, FNWI), Stochastic Operations Research, Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Background process Computer science ComputingMilieux_LEGALASPECTSOFCOMPUTING 02 engineering and technology Bivariate analysis Management Science and Operations Research 01 natural sciences Industrial and Manufacturing Engineering Set (abstract data type) 010104 statistics & probability 0202 electrical engineering electronic engineering information engineering Applied mathematics ruin probability 0101 mathematics rare-event simulation Markov chain Series (mathematics) Stochastic process 020206 networking & telecommunications ComputingMilieux_GENERAL importance sampling Large deviations Large deviations theory Statistics Probability and Uncertainty Importance sampling |
| Zdroj: | Probability in the Engineering and Informational Sciences, 31(3), 265-283. Cambridge University Press Probability in the Engineering and Informational Sciences, 31(3), 265-283 |
| ISSN: | 0269-9648 |
| Popis: | This paper focuses on the evaluation of the probability that both components of a bivariate stochastic process ever simultaneously exceed some large level; a leading example is that of two Markov fluid queues driven by the same background process ever reaching the set (u, ∞)×(u, ∞), for u>0. Exact analysis being prohibitive, we resort to asymptotic techniques and efficient simulation, focusing on large values of u. The first contribution concerns various expressions for the decay rate of the probability of interest, which are valid under Gärtner–Ellis-type conditions. The second contribution is an importance-sampling-based rare-event simulation technique for the bivariate Markov modulated fluid model, which is capable of asymptotically efficiently estimating the probability of interest; the efficiency of this procedure is assessed in a series of numerical experiments. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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