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020 _a9783319043944
_9978-3-319-04394-4
024 7 _a10.1007/978-3-319-04394-4
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
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072 7 _aPBT
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_2thema
082 0 4 _a519.2
_223
100 1 _aBurdzy, Krzysztof.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aBrownian Motion and its Applications to Mathematical Analysis
_h[electronic resource] :
_bÉcole d'Été de Probabilités de Saint-Flour XLIII – 2013 /
_cby Krzysztof Burdzy.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXII, 137 p. 16 illus., 4 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2106
505 0 _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.
520 _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.
650 0 _aDistribution (Probability theory.
650 0 _aDifferential equations, partial.
650 0 _aPotential theory (Mathematics).
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aPotential Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12163
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319043951
776 0 8 _iPrinted edition:
_z9783319043937
776 0 8 _iPrinted edition:
_z9783319709475
830 0 _aÉcole d'Été de Probabilités de Saint-Flour,
_x0721-5363 ;
_v2106
856 4 0 _uhttps://doi.org/10.1007/978-3-319-04394-4
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10890
_d10890