000 | 03387nam a22005295i 4500 | ||
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001 | 978-3-319-04394-4 | ||
003 | DE-He213 | ||
005 | 20190213151511.0 | ||
007 | cr nn 008mamaa | ||
008 | 140207s2014 gw | s |||| 0|eng d | ||
020 |
_a9783319043944 _9978-3-319-04394-4 |
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024 | 7 |
_a10.1007/978-3-319-04394-4 _2doi |
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050 | 4 | _aQA273.A1-274.9 | |
050 | 4 | _aQA274-274.9 | |
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_aPBT _2bicssc |
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_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. |
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300 |
_aXII, 137 p. 16 illus., 4 illus. in color. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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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 | ||
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