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Large deviation for diffusions and Hamilton-Jacobi equation in Hilbert spaces
dc.contributor.author | Feng, Jin | |
dc.date.accessioned | 2015-02-18T21:33:23Z | |
dc.date.available | 2015-02-18T21:33:23Z | |
dc.date.issued | 2006-01-01 | |
dc.identifier.citation | Feng, Jin. "Large deviation for diffusions and Hamilton-Jacobi equation in Hilbert spaces." The Annals of Probability. (2006) 34, 1. 321-385. http://dx.doi.org/10.1214/009117905000000567. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/16715 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1214/009117905000000567. | en_US |
dc.description.abstract | Large deviation for Markov processes can be studied by Hamilton– Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton–Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) holds for the limit equation. Finally, we verify an exponential compact containment estimate. The large deviation principle then follows from the above three verifications. This paper illustrates such a method applied to a class of Hilbert-spacevalued small diffusion processes. The examples include stochastically perturbed Allen–Cahn, Cahn–Hilliard PDEs and a one-dimensional quasilinear PDE with a viscosity term.We prove the comparison principle using a variant of the Tataru method. We also discuss different notions of viscosity solution in infinite dimensions in such context. | en_US |
dc.publisher | Institute of Mathematical Statistics | en_US |
dc.subject | large deviation | en_US |
dc.subject | stochastic evolution equation in Hilbert space | en_US |
dc.subject | viscosity solution of Hamilton-Jacobi equations | en_US |
dc.title | Large deviation for diffusions and Hamilton-Jacobi equation in Hilbert spaces | en_US |
dc.type | Article | |
kusw.kuauthor | Feng, Jin | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1214/009117905000000567 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess |