Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes

DOI10.1287/moor.2018.0950OpenAlexW2963410938WikidataQ127824952 ScholiaQ127824952MaRDI QIDQ5108224

Bohan Chen, Chang-Han Rhee, Bert Zwart, Jose H. Blanchet

Publication date: 30 April 2020

Published in: Mathematics of Operations Research (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.03981

zbMATH Keywords

random walkscompound Poisson processesrare-event simulationstrong efficiencyregularly varying distributionlarge deviations resultsprinciple of multiple big jumps

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Extreme value theory; extremal stochastic processes (60G70) Monte Carlo methods (65C05) Sums of independent random variables; random walks (60G50) Queueing theory (aspects of probability theory) (60K25) Large deviations (60F10)

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Cites Work

• Unnamed Item
• On the convergence from discrete to continuous time in an optimal stopping problem.
• Importance sampling for Jackson networks
• Efficient rare-event simulation for the maximum of heavy-tailed random walks
• Reflected Brownian motion on an orthant
• Counterexamples in importance sampling for large deviations probabilities
• Queues and Lévy fluctuation theory
• Dynamic importance sampling for queueing networks
• Simulating the ruin probability of risk processes with delay in claim settlement
• Heavy tails in multi-server queue
• Stochastic simulation: Algorithms and analysis
• A Subsidy-Surplus Model and the Skorokhod Problem in an Orthant
• Stochastic-Process Limits
• Semiparametric cross entropy for rare-event simulation
• On Large Delays in Multi-Server Queues with Heavy Tails
• Efficient importance sampling in ruin problems for multidimensional regularly varying random walks
• State-dependent importance sampling for regularly varying random walks
• Importance sampling for sums of random variables with regularly varying tails
• Importance Sampling, Large Deviations, and Differential Games
• Tail probabilities for non-standard risk and queueing processes with subexponential jumps
• Analysis of an importance sampling estimator for tandem queues
• An Introduction to Heavy-Tailed and Subexponential Distributions
• Markov Chain Monte Carlo for Computing Rare-Event Probabilities for a Heavy-Tailed Random Walk
• Stochastic Equations for Diffusion Processes in a Bounded Region. II

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