Stochastic Ordinary and Stochastic Partial Differential Equations

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Kotelenez, Peter. Stochastic Ordinary and Stochastic Partial Differential Equations Transition from Microscopic to Macroscopic Equations / by Peter Kotelenez. -
X, 459 p. online resource. - (Stochastic Modelling and Applied Probability, 58) Content notes : 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. 9780387743172 * Global analysis (Mathematics). Distribution (Probability theory. Mathematical physics. Analysis. Probability Theory and Stochastic Processes. Mathematical Methods in Physics. * Series