LEADER 03996nam 22007095 450 001 9910300143903321 005 20200630090111.0 010 $a3-319-04394-3 024 7 $a10.1007/978-3-319-04394-4 035 $a(CKB)3710000000089141 035 $a(DE-He213)978-3-319-04394-4 035 $a(SSID)ssj0001187031 035 $a(PQKBManifestationID)11659211 035 $a(PQKBTitleCode)TC0001187031 035 $a(PQKBWorkID)11240559 035 $a(PQKB)10699641 035 $a(MiAaPQ)EBC3107024 035 $a(PPN)176751084 035 $a(EXLCZ)993710000000089141 100 $a20140207d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBrownian Motion and its Applications to Mathematical Analysis$b[electronic resource] $eÉcole d'Été de Probabilités de Saint-Flour XLIII ? 2013 /$fby Krzysztof Burdzy 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (XII, 137 p. 16 illus., 4 illus. in color.) 225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2106 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-04393-5 320 $aIncludes bibliographical references (pages 133-137). 327 $a1. 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. 330 $aThese lecture notes provide an introduction to the applications of Brownian motion to analysis and, more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics. The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains. 410 0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2106 606 $aProbabilities 606 $aPartial differential equations 606 $aPotential theory (Mathematics) 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 615 0$aProbabilities. 615 0$aPartial differential equations. 615 0$aPotential theory (Mathematics). 615 14$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 615 24$aPotential Theory. 676 $a530.475 686 $aMAT 606f$2stub 686 $aMAT 607f$2stub 686 $aSI 850$2rvk 686 $a60J65$a60H30$a60G17$2msc 700 $aBurdzy$b Krzysztof$4aut$4http://id.loc.gov/vocabulary/relators/aut$059868 712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(43rd :$f2013 :$eSaint Flour, France) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300143903321 996 $aBrownian motion and its applications to mathematical analysis$9821272 997 $aUNINA