Karthyek R. A. Murthy, Sandeep Juneja, Jose Blanchet (2014) State-independent Importance Sampling for Random Walks with Regularly Varying Increments. Stochastic Systems 4(2):321-374. https://doi.org/10.1287/13-SSY114

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Abstract

We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation probabilities, 2) the level crossing probabilities, and 3) the level crossing probabilities within a regenerative cycle. Exponential twisting based state-independent methods, which are effective in efficiently estimating these probabilities for light-tailed increments are not applicable when the increments are heavy-tailed. To address the latter case, more complex and elegant state-dependent efficient simulation algorithms have been developed in the literature over the last few years. We propose that by suitably decomposing these rare event probabilities into a dominant and further residual components, simpler state-independent importance sampling algorithms can be devised for each …

Authors
Karthyek RA Murthy, Sandeep Juneja, Jose Blanchet
Publication date
2015/3
Journal
Stochastic Systems
Volume
4
Issue
2
Pages
321-374
Publisher
INFORMS