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Probability and Partial Differential Equations in Modern Applied Mathematics

Publisher: 
Springer Verlag
Number of Pages: 
262
Price: 
79.95
ISBN: 
0-387-25879-5
Date Received: 
Wednesday, September 14, 2005
Reviewable: 
Include In BLL Rating: 
Reviewer Email Address: 
Edward C. Waymire and Jinqiao Duan, editors
Series: 
The IMA Volumes in Mathematics and Its Applications 140
Publication Date: 
2005
Format: 
Hardcover
Category: 
Monograph

 Forward.- Preface.- Nonnegative Markov chains with appliations.- Phase changes with time and multi-scale homogenizations of a class of anomalous diffusions.- Semi-Markov cascade representations of local solutions to 3-D incompressible Navier-Stokes.- Amplitude equations for SPDEs: Approximate centre manifolds and invariant measures.- Enstrophy and ergodicity of gravity currents.- Stochastic heat and Burgers equations and their singularities.- A gentle introduction to cluster expansions.- Continuity of the Ito-map for Holder rough paths with applications to the Support Theorem in Holder norm.- Data-driven stochastic processes in fully developed turbulence.- Stochastic flows on the circle.- Path integration: connecting pure jump and Wiener processes.- Random dynamical systems in economics.- A geometric cascade for the spectral approximation of the Navier-Stokes equations.- Inertial manifolds for random differential equations.- Existence and uniqueness of classical, nonnegative, smooth solutions of a class of semi-linear SPDEs.- Nonlinear PDE's driven by Levy diffusions and related statistical issues.- List of workshop participants.

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Wednesday, September 14, 2005

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