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Rare-event Simulation for Multidimensional Regularly Varying Random Walks
| Content Provider | Semantic Scholar |
|---|---|
| Author | Blanchet, José H. Liu, Jingchen |
| Copyright Year | 2009 |
| Abstract | We consider the problem of e¢ cient estimation via simulation of rst passage time probabilities for a multidimensional random walk with regularly varying increments. In addition of being a natural generalization of the problem of computing ruin probabilities in insurance in which the focus is a one dimensional random walk this problem captures important features of large deviations for multidimensional heavy-tailed processes (such as the role played by the mean of the process in connection to the location of the target set). We develop a state-dependent importance sampling estimator for this class of multidimensional problems. Then, we argue using techniques based on Lyapunov inequalities that our estimator is strongly e¢ cient in the sense that the mean square error of our estimator can be made arbitrarily small by increasing the number of replications, uniformly as the probability of interest approaches zero. An important feature of our algorithm involves the interplay between large deviations for regularly varying processes and linear programming. When the target set is the union of half-spaces, our sampler, which can be described in terms of mixtures, can be shown to approximate in total variation the conditional distribution of the walk given that it hits the target set in nite time. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.columbia.edu/~jb2814/papers/HighDimJournal6.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
