04167nam a22004455i 4500 978-0-387-74317-2 DE-He213 20260521091948.0 cr nn 008mamaa 100301s2008 xxu| s |||| 0|eng d 9780387743172 99780387743172 10.1007/978-0-387-74317-2 doi CICY 519.2 23 Kotelenez, Peter. author. Stochastic Ordinary and Stochastic Partial Differential Equations [recurso electrónico] : Transition from Microscopic to Macroscopic Equations / by Peter Kotelenez. New York, NY : Springer New York, 2008. online resource. text txt rdacontent computer c rdamedia recurso en línea cr rdacarrier text file PDF rda Stochastic Modelling and Applied Probability formerly: Applications of Mathematics, 0172-4568 ; 58 From 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. This 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. MATHEMATICS. DISTRIBUTION (PROBABILITY THEORY). MATHEMATICAL PHYSICS. MATHEMATICS. PROBABILITY THEORY AND STOCHASTIC PROCESSES. MATHEMATICAL METHODS IN PHYSICS. SpringerLink (Online service) Springer eBooks Printed edition: 9780387743165 Stochastic Modelling and Applied Probability formerly: Applications of Mathematics, 0172-4568 ; 58 http://dx.doi.org/10.1007/978-0-387-74317-2 Ver el texto completo en las instalaciones del CICY ddc ER 34511 34511 0 0 ddc 0 0 LE CICY CICY EL 2025-07-10 0 519.2 2025-07-10 08:40:19 2025-07-10 ER