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Large deviations an...
Large deviations and fast simulation in the presence of boundaries
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- Asmussen, Sören (author)
- Lund University,Lunds universitet,Matematisk statistik,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematical Statistics,Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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Fuckerieder, P (author)
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Jobmann, M (author)
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Schwefel, HP (author)
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(creator_code:org_t)
- 2002
- 2002
- English.
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In: Stochastic Processes and their Applications. - 1879-209X. ; 102:1, s. 1-23
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Abstract
Subject headings
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- Let c(x) = inf {t > 0: Q(t) greater than or equal to x} be the time of first overflow of a queueing process 1001 over level x (the buffer size) and Z = P(T(X) less than or equal to T). Assuming that {Q(t)) is the reflected version of a Levy process {X(t)} or a Markov additive process, we study a variety of algorithms for estimating z by simulation when the event {tau(X) less than or equal to T} is rare, and analyse their performance. In particular, we exhibit an estimator using a filtered Monte Carlo argument which is logarithmically efficient whenever an efficient estimator for the probability of overflow within a busy cycle (i.e., for first passage probabilities for the unrestricted netput process) is available, thereby providing a way out of counterexamples in the literature on the scope of the large deviations approach to rare events simulation. We also add a counterexample of this type and give various theoretical results on asymptotic properties of Z=P(tau(x) less than or equal to T), both in the reflected Levy process setting and more generally for regenerative processes in a regime where T is so small that the exponential approximation for T(x) is not a priori valid.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- rare
- queueing theory
- local time
- Levy process
- importance sampling
- filtered Monte Carlo
- buffer overflow
- exponential change of measure
- event
- reflection
- regenerative process
- saddlepoint
Publication and Content Type
- art (subject category)
- ref (subject category)
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