04057nam a22004095i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003500137040000900172082001400181100003100195245017400226264004600400300002100446336002600467337002600493338003900519347002400558490010500582505106000687520141701747650001703164650003903181650002603220650001703246650004903263650003703312710003403349773002003383776003603403830010503439856010303544978-0-387-74317-2DE-He21320260521091948.0cr nn 008mamaa100301s2008    xxu|    s    |||| 0|eng d  a9780387743172  a997803877431727 a10.1007/978-0-387-74317-22doi  cCICY04a519.22231 aKotelenez, Peter.eauthor.10aStochastic Ordinary and Stochastic Partial Differential Equationsh[recurso electrónico] :bTransition from Microscopic to Macroscopic Equations /cby Peter Kotelenez. 1aNew York, NY :bSpringer New York,c2008.  bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  arecurso en líneabcr2rdacarrier  atext filebPDF2rda1 aStochastic Modelling and Applied Probability formerly: Applications of Mathematics,x0172-4568 ;v580 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.  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. 0aMATHEMATICS. 0aDISTRIBUTION (PROBABILITY THEORY). 0aMATHEMATICAL PHYSICS.14aMATHEMATICS.24aPROBABILITY THEORY AND STOCHASTIC PROCESSES.24aMATHEMATICAL METHODS IN PHYSICS.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387743165 0aStochastic Modelling and Applied Probability formerly: Applications of Mathematics,x0172-4568 ;v5840uhttp://dx.doi.org/10.1007/978-0-387-74317-2zVer el texto completo en las instalaciones del CICY