Matches in SemOpenAlex for { <https://semopenalex.org/work/W2424614260> ?p ?o ?g. }
- W2424614260 abstract "After the brilliant result of Papanicolau and Varadhan (1979) in the case of bounded stationary and ergodic environments, there has been a recent upsurge in the research of quenched homogenization of a symmetric diffusion process in random media. In particular, to identify the optimal conditions that a general stationary and ergodic environment must satisfy in order to obtain the convergence to a non-degenerate Brownian motion, is still an open problem. In this manuscript we show that, provided that the environment satisfies certain moment conditions, then both a quenched invariance principle and a quenched local central limit theorem hold for a diffusion formally generated by the divergence form operator L = div(a∇· ). Since the coefficients are not assumed to be smooth, we shall exploit Dirichlet form theory to make sense of the diffusion associated to L. Both the proofs of the quenched invariance principle and of the quenched local central limit theorem rely on a priori estimates for solutions to linear partial differential equations. On one hand, with the help of the celebrated J. Moser’s iteration technique, we derive a maximal inequality for solutions to degenerate elliptic PDEs which in turn gives the sublinearity of the correctors and with that the quenched invariance principle. On the other hand, relying once again on Moser’s scheme, we obtain a parabolic Harnack inequality which can be used to control the oscillations of solutions to parabolic PDEs. In particular, in the diffusive limit, we are able to bound the oscillations of the transition densities of our diffusion. This successively yields the quenched local central limit theorem." @default.
- W2424614260 created "2016-06-24" @default.
- W2424614260 creator A5043409584 @default.
- W2424614260 date "2015-09-25" @default.
- W2424614260 modified "2023-09-24" @default.
- W2424614260 title "Invariance principle for diffusions in degenerate and unbounded random environment" @default.
- W2424614260 cites W104863772 @default.
- W2424614260 cites W1480737658 @default.
- W2424614260 cites W1501523395 @default.
- W2424614260 cites W1520461790 @default.
- W2424614260 cites W1544375930 @default.
- W2424614260 cites W1545370368 @default.
- W2424614260 cites W1582706191 @default.
- W2424614260 cites W1731882074 @default.
- W2424614260 cites W179959538 @default.
- W2424614260 cites W1866311589 @default.
- W2424614260 cites W1974309308 @default.
- W2424614260 cites W1986379750 @default.
- W2424614260 cites W2008280709 @default.
- W2424614260 cites W2015740403 @default.
- W2424614260 cites W2023324267 @default.
- W2424614260 cites W2033862281 @default.
- W2424614260 cites W2051772151 @default.
- W2424614260 cites W2052737041 @default.
- W2424614260 cites W2149461673 @default.
- W2424614260 cites W2231106691 @default.
- W2424614260 cites W2314750725 @default.
- W2424614260 cites W2357029327 @default.
- W2424614260 cites W3021722416 @default.
- W2424614260 cites W352297584 @default.
- W2424614260 cites W628921719 @default.
- W2424614260 cites W958989108 @default.
- W2424614260 doi "https://doi.org/10.14279/depositonce-4723" @default.
- W2424614260 hasPublicationYear "2015" @default.
- W2424614260 type Work @default.
- W2424614260 sameAs 2424614260 @default.
- W2424614260 citedByCount "0" @default.
- W2424614260 crossrefType "dissertation" @default.
- W2424614260 hasAuthorship W2424614260A5043409584 @default.
- W2424614260 hasConcept C105795698 @default.
- W2424614260 hasConcept C112401455 @default.
- W2424614260 hasConcept C118365987 @default.
- W2424614260 hasConcept C121332964 @default.
- W2424614260 hasConcept C122044880 @default.
- W2424614260 hasConcept C126255220 @default.
- W2424614260 hasConcept C130217890 @default.
- W2424614260 hasConcept C134306372 @default.
- W2424614260 hasConcept C138885662 @default.
- W2424614260 hasConcept C156387681 @default.
- W2424614260 hasConcept C163072092 @default.
- W2424614260 hasConcept C166785042 @default.
- W2424614260 hasConcept C18903297 @default.
- W2424614260 hasConcept C2778722038 @default.
- W2424614260 hasConcept C3017618536 @default.
- W2424614260 hasConcept C31010330 @default.
- W2424614260 hasConcept C33923547 @default.
- W2424614260 hasConcept C34388435 @default.
- W2424614260 hasConcept C41008148 @default.
- W2424614260 hasConcept C41895202 @default.
- W2424614260 hasConcept C56739046 @default.
- W2424614260 hasConcept C62520636 @default.
- W2424614260 hasConcept C68710425 @default.
- W2424614260 hasConcept C70610323 @default.
- W2424614260 hasConcept C72319582 @default.
- W2424614260 hasConcept C8464174 @default.
- W2424614260 hasConcept C86803240 @default.
- W2424614260 hasConcept C91575142 @default.
- W2424614260 hasConceptScore W2424614260C105795698 @default.
- W2424614260 hasConceptScore W2424614260C112401455 @default.
- W2424614260 hasConceptScore W2424614260C118365987 @default.
- W2424614260 hasConceptScore W2424614260C121332964 @default.
- W2424614260 hasConceptScore W2424614260C122044880 @default.
- W2424614260 hasConceptScore W2424614260C126255220 @default.
- W2424614260 hasConceptScore W2424614260C130217890 @default.
- W2424614260 hasConceptScore W2424614260C134306372 @default.
- W2424614260 hasConceptScore W2424614260C138885662 @default.
- W2424614260 hasConceptScore W2424614260C156387681 @default.
- W2424614260 hasConceptScore W2424614260C163072092 @default.
- W2424614260 hasConceptScore W2424614260C166785042 @default.
- W2424614260 hasConceptScore W2424614260C18903297 @default.
- W2424614260 hasConceptScore W2424614260C2778722038 @default.
- W2424614260 hasConceptScore W2424614260C3017618536 @default.
- W2424614260 hasConceptScore W2424614260C31010330 @default.
- W2424614260 hasConceptScore W2424614260C33923547 @default.
- W2424614260 hasConceptScore W2424614260C34388435 @default.
- W2424614260 hasConceptScore W2424614260C41008148 @default.
- W2424614260 hasConceptScore W2424614260C41895202 @default.
- W2424614260 hasConceptScore W2424614260C56739046 @default.
- W2424614260 hasConceptScore W2424614260C62520636 @default.
- W2424614260 hasConceptScore W2424614260C68710425 @default.
- W2424614260 hasConceptScore W2424614260C70610323 @default.
- W2424614260 hasConceptScore W2424614260C72319582 @default.
- W2424614260 hasConceptScore W2424614260C8464174 @default.
- W2424614260 hasConceptScore W2424614260C86803240 @default.
- W2424614260 hasConceptScore W2424614260C91575142 @default.
- W2424614260 hasLocation W24246142601 @default.
- W2424614260 hasOpenAccess W2424614260 @default.
- W2424614260 hasPrimaryLocation W24246142601 @default.
- W2424614260 hasRelatedWork W1007281767 @default.
- W2424614260 hasRelatedWork W1976083053 @default.