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Importance sampling of heavy-tailed iterated random functions
| Content Provider | Scilit |
|---|---|
| Author | Chen, Bohan Rhee, Chang-Han Zwart, Bert |
| Copyright Year | 2018 |
| Description | We consider the stationary solutionZof the Markov chain ${Z_{n}}_{n∈ℕ}$defined $byZ_{n+1}=ψ_{n+1}(Z_{n}$), where ${ψ_{n}}_{n∈ℕ}$is a sequence of independent and identically distributed random Lipschitz functions. We estimate the probability of the event {Z>x} whenxis large, and develop a state-dependent importance sampling estimator under a set of assumptions on $ψ_{n}$such that, for largex, the event {Z>x} is governed by a single large jump. Under natural conditions, we show that our estimator is strongly efficient. Special attention is paid to a class of perpetuities with heavy tails. |
| Related Links | http://arxiv.org/pdf/1609.03182 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A45C7CE80945A169903BE977715613EF/S000186781800037Xa.pdf/div-class-title-importance-sampling-of-heavy-tailed-iterated-random-functions-div.pdf |
| Ending Page | 832 |
| Page Count | 28 |
| Starting Page | 805 |
| ISSN | 00018678 |
| e-ISSN | 14756064 |
| DOI | 10.1017/apr.2018.37 |
| Journal | Advances in Applied Probability |
| Issue Number | 3 |
| Volume Number | 50 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2018-09-01 |
| Access Restriction | Open |
| Subject Keyword | Advances in Applied Probability Applied Mathematics dependent Importance Sampling tailed Distribution Iterated Random Function |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability |
