000 | 03328nam a22004815i 4500 | ||
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001 | 978-3-540-46587-4 | ||
003 | DE-He213 | ||
005 | 20190213151804.0 | ||
007 | cr nn 008mamaa | ||
008 | 100730s2000 gw | s |||| 0|eng d | ||
020 |
_a9783540465874 _9978-3-540-46587-4 |
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024 | 7 |
_a10.1007/BFb0112488 _2doi |
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072 | 7 |
_aPBK _2bicssc |
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_aMAT034000 _2bisacsh |
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_aPBK _2thema |
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082 | 0 | 4 |
_a515 _223 |
100 | 1 |
_aKolokoltsov, Vassili N. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aSemiclassical Analysis for Diffusions and Stochastic Processes _h[electronic resource] / _cby Vassili N. Kolokoltsov. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c2000. |
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300 |
_aVIII, 356 p. _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 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1724 |
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505 | 0 | _aGaussian diffusions -- Boundary value problem for Hamiltonian systems -- Semiclassical approximation for regular diffusion -- Invariant degenerate diffusion on cotangent bundles -- Transition probability densities for stable jump-diffusions -- Semiclassical asymptotics for the localised Feller-Courrège processes -- Complex stochastic diffusion or stochastic Schrödinger equation -- Some topics in semiclassical spectral analysis -- Path integration for the Schrödinger, heat and complex diffusion equations. | |
520 | _aThe monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus. | ||
650 | 0 | _aGlobal analysis (Mathematics). | |
650 | 0 | _aDistribution (Probability theory. | |
650 | 1 | 4 |
_aAnalysis. _0http://scigraph.springernature.com/things/product-market-codes/M12007 |
650 | 2 | 4 |
_aProbability Theory and Stochastic Processes. _0http://scigraph.springernature.com/things/product-market-codes/M27004 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783540669722 |
776 | 0 | 8 |
_iPrinted edition: _z9783662169087 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1724 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0112488 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
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