03996nam 22007095 450 991030014390332120200630090111.03-319-04394-310.1007/978-3-319-04394-4(CKB)3710000000089141(DE-He213)978-3-319-04394-4(SSID)ssj0001187031(PQKBManifestationID)11659211(PQKBTitleCode)TC0001187031(PQKBWorkID)11240559(PQKB)10699641(MiAaPQ)EBC3107024(PPN)176751084(EXLCZ)99371000000008914120140207d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierBrownian Motion and its Applications to Mathematical Analysis[electronic resource] École d'Été de Probabilités de Saint-Flour XLIII – 2013 /by Krzysztof Burdzy1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (XII, 137 p. 16 illus., 4 illus. in color.) École d'Été de Probabilités de Saint-Flour,0721-5363 ;2106Bibliographic Level Mode of Issuance: Monograph3-319-04393-5 Includes bibliographical references (pages 133-137).1. Brownian motion -- 2. Probabilistic proofs of classical theorems -- 3. Overview of the "hot spots" problem -- 4. Neumann eigenfunctions and eigenvalues -- 5. Synchronous and mirror couplings -- 6. Parabolic boundary Harnack principle -- 7. Scaling coupling -- 8. Nodal lines -- 9. Neumann heat kernel monotonicity -- 10. Reflected Brownian motion in time dependent domains.These lecture notes provide an introduction to the applications of Brownian motion to analysis and, more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics. The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains.École d'Été de Probabilités de Saint-Flour,0721-5363 ;2106ProbabilitiesPartial differential equationsPotential theory (Mathematics)Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Potential Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12163Probabilities.Partial differential equations.Potential theory (Mathematics).Probability Theory and Stochastic Processes.Partial Differential Equations.Potential Theory.530.475MAT 606fstubMAT 607fstubSI 850rvk60J6560H3060G17mscBurdzy Krzysztofauthttp://id.loc.gov/vocabulary/relators/aut59868Ecole d'été de probabilités de Saint-Flour(43rd :2013 :Saint Flour, France)MiAaPQMiAaPQMiAaPQBOOK9910300143903321Brownian motion and its applications to mathematical analysis821272UNINA