For some families of one-dimensional locally infinitely divisible Markov processes xet 0≤t≤T with frequent small jumps, large deviation expansions for expectations are proved: as epsilon ↓ 0 Ee expe-1F xe =expe -1Ff0 -Sf0 0≤i≤ s/2Ki˙ei+o&parl0; es/2&parr0; where s is a positive integer, S is the normalized action functional, constants Ki are expressed through derivatives of the smooth functional F, and &phis;0 is the unique maximizer of F -- S The proof of above large deviation expansions relies on asymptotic expansions for expectations of a smooth functional G of stochastic processes etaepsilon = epsilon--1/2(xi epsilon -- &phis;0) : as epsilon ↓ 0 EeGhe =EGh +e1/2EA1Gh +˙˙˙+es/2EAsG h+o&parl0;es/2&parr0; for some Gaussian diffusion eta and suitable differential operators Ai / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_27350 |
| Date | January 2011 |
| Contributors | Yang, Xiangfeng (Author), Didier, Gustavo (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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