State-independent Importance Sampling for Random Walks with Regularly Varying Increments
Published Online:13 Oct 2014https://doi.org/10.1287/13-SSY114
References
- Adler, R. J., Feldman, R. E., and Taqqu, M. S., Eds. (1998). A Practical Guide to Heavy Tails. Birkhäuser Boston Inc., Boston, MA. Statistical techniques and applications. MR1652283Google Scholar
- (2013). Efficient simulation of large deviation events for sums of random vectors using saddle-point representations. Journal of Applied Probability 50, 3 (09), 703–720. http://dx.doi.org/10.1239/jap/1378401231. MR3102510Google Scholar
- (1998). Subexponential asymptotics for stochastic processes: extremal behavior, stationary distributions and first passage probabilities. The Annals of Applied Probability 8, 2 (05), 354–374. http://dx.doi.org/10.1214/aoap/1028903531. MR1624933Google Scholar
- (2000). Rare events simulation for heavy-tailed distributions. Bernoulli 6, 2, 303–322. MR1748723Google Scholar
- (2007). Stochastic Simulation: Algorithms and Analysis. Stochastic Modelling and Applied Probability, Vol. 57. Springer, New York. MR2331321Google Scholar
- (1996). Large deviations results for subexponential tails, with applications to insurance risk. Stochastic Processes and Their Applications 64, 1, 103–125. MR1419495Google Scholar
- (2006). Improved algorithms for rare event simulation with heavy tails. Adv. in Appl. Probab. 38, 2, 545–558. MR2264957Google Scholar
- (2007). On the inefficiency of state-independent importance sampling in the presence of heavy tails. Oper. Res. Lett. 35, 2, 251–260. MR2311409Google Scholar
- (2008). Portfolio credit risk with extremal dependence: Asymptotic analysis and efficient simulation. Operations Research 56, 3, 593–606. MR2436855Link, Google Scholar
- (2008). Efficient rare-event simulation for the maximum of heavy-tailed random walks. Ann. Appl. Probab. 18, 4, 1351–1378. MR2434174Google Scholar
- (2007). Fluid heuristics, Lyapunov bounds and efficient importance sampling for a heavy-tailed G/G/1 queue. Queueing Systems 57, 2–3, 99–113. MR2358076Google Scholar
- (2009). Efficient simulation of light-tailed sums: An old-folk song sung to a faster new tune… In Monte Carlo and Quasi-Monte Carlo Methods 2008. Springer, Berlin, 227–248. MR2743897Google Scholar
- (2008). State-dependent importance sampling for regularly varying random walks. Adv. in Appl. Probab. 40, 4, 1104–1128. MR2488534Google Scholar
- (2012). Efficient simulation and conditional functional limit theorems for ruinous heavy-tailed random walks. Stochastic Processes and Their Applications 122, 8, 2994–3031. MR2931349Google Scholar
- (2002). On probabilities of large deviations for random walks I. Regularly varying distribution tails. Theory of Probability and Its Applications 46, 2, 193–213. http://epubs.siam.org/doi/abs/10.1137/S0040585X97978877.Google Scholar
- (2008). Asymptotic Analysis of Random Walks. Encyclopedia of Mathematics and Its Applications, Vol. 118. Cambridge University Press, Cambridge. MR2424161Google Scholar
- (2001). On large deviation probabilities of random walks with heavy tails. Preprint EURANDOM, Eindhoven. MR1994823Google Scholar
- (2012). Rare-event simulation of heavy-tailed random walks by sequential importance sampling and resampling. Advances in Applied Probability 44, 4 (12), 1173–1196. http://dx.doi.org/10.1239/aap/1354716593. MR3052853Google Scholar
- (1991). Large deviation probabilities for sums and maxima of random variables with heavy or subexponential tails. Preprint, Texas A&M University 501.Google Scholar
- (2007). Local asymptotics of the cycle maximum of a heavy-tailed random walk. Advances in Applied Probability 39, 1 (03), 221–244. http://dx.doi.org/10.1239/aap/1175266476. MR2307878Google Scholar
- (2005). On asymptotically efficient simulation of large deviation probabilities. Adv. in Appl. Probab. 37, 2, 539–552. MR2144566Google Scholar
- (2007). Importance sampling for sums of random variables with regularly varying tails. ACM Trans. Model. Comput. Simul. 17, 3 (July).Google Scholar
- (2004). Importance sampling, large deviations, and differential games. Stoch. Stoch. Rep. 76, 6, 481–508. MR2100018Google Scholar
- (1997). Modelling Extremal Events. Applications of Mathematics (New York), Vol. 33. Springer-Verlag, Berlin. For insurance and finance. MR1458613Google Scholar
- (1971). An Introduction to Probability Theory and Its Applications Volume II. Wiley. MR0270403Google Scholar
- (2011). An Introduction to Heavy-Tailed and Subexponential Distributions. Springer Series in Operations Research and Financial Engineering. Springer, New York. MR2810144Google Scholar
- (2005). Importance sampling for portfolio credit risk. Management Science 51, 11, 1643–1656.Link, Google Scholar
- (1992). The asymptotic efficiency of simulation estimators. Oper. Res. 40, 3, 505–520. MR1180030Link, Google Scholar
- (1965). Monte Carlo Methods. Methuen & Co. Ltd., London. MR0223065Google Scholar
- (2007). Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error. Queueing Syst. 57, 2–3, 115–127. MR2358077Google Scholar
- (2002). Simulating heavy tailed processes using delayed hazard rate twisting. ACM Trans. Model. Comput. Simul. 12, 2 (Apr.), 94–118.Google Scholar
- (2006). Rare event simulation techniques: An introduction and recent advances. Simulation, Handbooks in Operations Research and Management Science, 291–350.Google Scholar
- (1997). On distribution tail of the maximum of a random walk. Stochastic Processes and Their Applications 72, 1, 97–103. http://www.sciencedirect.com/science/article/pii/S0304414997000604. MR1483613Google Scholar
- (2012). State-independent importance sampling for estimating large deviation probabilities in heavy-tailed random walks. In Performance Evaluation Methodologies and Tools (VALUETOOLS), 2012. 127–135.Google Scholar
- (1989). A quick simulation method for excessive backlogs in networks of queues. IEEE Trans. Automat. Control 34, 1, 54–66. MR0970932Google Scholar
- (1997). Heavy tail modeling and teletraffic data. Ann. Statist. 25, 5, 1805–1869. With discussion and a rejoinder by the author. MR1474072Google Scholar
- (1996). On Monte Carlo estimation of large deviations probabilities. Ann. Appl. Probab. 6, 2, 399–422. MR1398051Google Scholar
- (1990). On large deviations theory and asymptotically efficient Monte Carlo estimation. IEEE Trans. Inform. Theory 36, 3, 579–588. MR1053850Google Scholar
- (1976). Importance sampling in the Monte Carlo study of sequential tests. Ann. Statist. 4, 4, 673–684. MR0418369Google Scholar
- (1977). Asymptotic behaviour of Wiener-Hopf factors of a random walk. Stochastic Processes and Their Applications 5, 1, 27–37. MR0423543Google Scholar

