Stochastic Analysis and Partial Differential Equations

Erscheinungsjahr 2007
ISBN: 978-0-8218-4059-7
Verlag: American Mathematical Society

Buch, Englisch, Band 429, 285 Seiten, Gewicht: 510 g

Reihe: Contemporary Mathematics

This book is a collection of original research papers and expository articles from the scientific program of the 2004-05 Emphasis Year on Stochastic Analysis and Partial Differential Equations at Northwestern University. Many well-known mathematicians attended the events and submitted their contributions for this volume. Topics from stochastic analysis discussed in this volume include stochastic analysis of turbulence, Markov processes, microscopic lattice dynamics, microscopic interacting particle systems, and stochastic analysis on manifolds. Topics from partial differential equations include kinetic equations, hyperbolic conservation laws, Navier-Stokes equations, and Hamilton-Jacobi equations. A variety of methods, such as numerical analysis, homogenization, measure-theoretical analysis, entropy analysis, weak convergence analysis, Fourier analysis, and Ito's calculus, are further developed and applied. All these topics are naturally interrelated and represent a cross-section of the most significant recent advances and current trends and directions in stochastic analysis and partial differential equations. This volume is suitable for researchers and graduate students interested in stochastic analysis, partial differential equations, and related analysis and applications.

Zielgruppe

Graduate students and research mathematicians interested in stochastic analysis and partical differential equations

Autoren/Hrsg.

Chen, Gui-Qiang

Hsu, Elton

Pinsky, Mark

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik

Inhaltsverzeichnis

Construction of suitable weak solutions of the Navier-Stokes equations, A. Biryuk, W. Craig, and S. Ibrahim

Error estimates for finite difference-quadrature schemes for a class of nonlocal Bellman equations with variable diffusion, I. H. Biswas, E. R. Jakobsen, and K. H. Karlsen

Recent progress in the stochastic analysis of turbulent mixing, W. Bo, B. Cheng, J. Du, B. Fix, E. George, J. Glimm, J. W. Grove, X. Jia, H. Jin, H. Lee, Y. Li, X. Li, X. Liu, D. H. Sharp, L. Wu, and Y. Yu

Modified Keller-Segel system and critical mass for the log interaction kernel, V. Calvez, B. Perthame, and M. S. tabar

Entropy solutions to conservation laws with discontinuous fluxes via microscopic interacting particle systems, G.-Q. Chen, N. Even, and C. Klingenberg

Spectral properties of subordinate processes in domains, Z.-Q. Chen and R. Song

Smoluchowski Navier-Stokes systems, P. Constantin

Recent developments in stochastic differential equations, S. Fang

Heat equations on manifolds and Bismut's formula, E. P. Hsu

On a class of one-dimensional Markov processes with continuous paths, N. Ikeda and Y. Ogura

Prototype hybrid couplings of macroscopic deterministic models and microscopic stochastic lattice dynamics, M. A. Katsoulakis, A. J. Majda, and A. Sopasakis

Homogenization of stochastic Hamilton-Jacobi equations: Brief review of methods and applications, E. Kosygina

General relative entropy in a nonlinear McKendrick model, P. Michel

Pointwise Fourier inversion in analysis and geometry, M. A. Pinsky

Stochastic analysis and the KdV equation, S. Taniguchi

On binary fluid mixtures, K. Trivisa

Über Autor(innen)

Gui-Qiang Chen, Northwestern University, Evanston, IL; Elton Hsu, Northwestern University, Evanston, IL;

Mark Pinsky, Northwestern University, Evanston, IL