000			04157nam a22004335i 4500
001			978-0-387-74317-2
003			DE-He213
005			20250710084019.0
007			cr nn 008mamaa
008			100301s2008 xxu| s |||| 0|eng d
020			_a9780387743172 _a99780387743172
024	7		_a10.1007/978-0-387-74317-2 _2doi
082	0	4	_a519.2 _223
100	1		_aKotelenez, Peter. _eauthor.
245	1	0	_aStochastic Ordinary and Stochastic Partial Differential Equations _h[recurso electrónico] : _bTransition from Microscopic to Macroscopic Equations / _cby Peter Kotelenez.
264		1	_aNew York, NY : _bSpringer New York, _c2008.
300			_bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aStochastic Modelling and Applied Probability formerly: Applications of Mathematics, _x0172-4568 ; _v58
505	0		_aFrom Microscopic Dynamics to Mesoscopic Kinematics -- Heuristics: Microscopic Model and Space-Time Scales -- Deterministic Dynamics in a Lattice Model and a Mesoscopic (Stochastic) Limit -- Proof of the Mesoscopic Limit Theorem -- Mesoscopic A: Stochastic Ordinary Differential Equations -- Stochastic Ordinary Differential Equations: Existence, Uniqueness, and Flows Properties -- Qualitative Behavior of Correlated Brownian Motions -- Proof of the Flow Property -- Comments on SODEs: A Comparison with Other Approaches -- Mesoscopic B: Stochastic Partial Differential Equations -- Stochastic Partial Differential Equations: Finite Mass and Extensions -- Stochastic Partial Differential Equations: Infinite Mass -- Stochastic Partial Differential Equations:Homogeneous and Isotropic Solutions -- Proof of Smoothness, Integrability, and Itô's Formula -- Proof of Uniqueness -- Comments on Other Approaches to SPDEs -- Macroscopic: Deterministic Partial Differential Equations -- Partial Differential Equations as a Macroscopic Limit -- General Appendix.
520			_aThis book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation. A detailed analysis of the SODEs and (quasi-linear) SPDEs is presented. Semi-linear (parabolic) SPDEs are represented as first order stochastic transport equations driven by Stratonovich differentials. The time evolution of correlated Brownian motions is shown to be consistent with the depletion phenomena experimentally observed in colloids. A covariance analysis of the random processes and random fields as well as a review section of various approaches to SPDEs are also provided. An extensive appendix makes the book accessible to both scientists and graduate students who may not be specialized in stochastic analysis. Probabilists, mathematical and theoretical physicists as well as mathematical biologists and their graduate students will find this book useful. Peter Kotelenez is a professor of mathematics at Case Western Reserve University in Cleveland, Ohio.
650		0	_aMATHEMATICS.
650		0	_aDISTRIBUTION (PROBABILITY THEORY).
650		0	_aMATHEMATICAL PHYSICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aPROBABILITY THEORY AND STOCHASTIC PROCESSES.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387743165
830		0	_aStochastic Modelling and Applied Probability formerly: Applications of Mathematics, _x0172-4568 ; _v58
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-74317-2 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c58575 _d58575