MARC Record from harvard_bibliographic_metadata

LEADER: 03628cam a22003374a 4500
001 011463246-4
005 20140910154234.0
008 071029s2008 nyu b 001 0 eng c
010 $a 2007940371
020 $a9780387743165
020 $a0387743162
035 0 $aocn172984133
040 $aBTCTA$cBTCTA$dDLC$dBAKER$dBET$dWAU$dOHX$dYDXCP$dIXA
042 $apcc
050 00 $aQA274.23$b.K68 2008
082 00 $a519.2$222
100 1 $aKotelenez, P.$q(Peter),$d1943-
245 10 $aStochastic ordinary and stochastic partial differential equations :$btransition from microscopic to macroscopic equations /$cPeter Kotelenez.
260 $aNew York :$bSpringer Science+Business Media,$cc2008.
300 $ax, 458 p. ;$c25 cm.
440 0 $aStochastic modelling and applied probability ;$v58
504 $aIncludes bibliographical references (p. 445-458) and index.
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 $aStochastic differential equations.
650 0 $aStochastic partial differential equations.
650 0 $aDistribution (Probability theory).
650 0 $aMathematical physics.
650 0 $aMathematics.
988 $a20080512
906 $0OCLC