Probabilistic Models For Nonlinear Partial Differential Equations
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Probabilistic Models For Nonlinear Partial Differential Equations
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Author : Carl Graham
language : en
Publisher: Springer
Release Date : 2006-11-13
Probabilistic Models For Nonlinear Partial Differential Equations written by Carl Graham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-13 with Mathematics categories.
The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems. This book, collecting the notes of these courses, will be useful to probabilists working on stochastic particle methods and on the approximation of SPDEs, in particular, to PhD students and young researchers.
Probabilistic Models For Nonlinear Partial Differential Equations
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Author :
language : en
Publisher:
Release Date : 1996
Probabilistic Models For Nonlinear Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Convergence categories.
Probability And Partial Differential Equations In Modern Applied Mathematics
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Author : Edward C. Waymire
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-14
Probability And Partial Differential Equations In Modern Applied Mathematics written by Edward C. Waymire and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-14 with Mathematics categories.
"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes. There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations. This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.
Calculus Of Variations And Nonlinear Partial Differential Equations
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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-02
Calculus Of Variations And Nonlinear Partial Differential Equations written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-02 with Mathematics categories.
With a historical overview by Elvira Mascolo
Three Classes Of Nonlinear Stochastic Partial Differential Equations
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Author : Jie Xiong
language : en
Publisher: World Scientific
Release Date : 2013-05-06
Three Classes Of Nonlinear Stochastic Partial Differential Equations written by Jie Xiong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-06 with Mathematics categories.
The study of measure-valued processes in random environments has seen some intensive research activities in recent years whereby interesting nonlinear stochastic partial differential equations (SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz continuity of their coefficients, new techniques and concepts have recently been developed for the study of such SPDEs. These include the conditional Laplace transform technique, the conditional mild solution, and the bridge between SPDEs and some kind of backward stochastic differential equations. This volume provides an introduction to these topics with the aim of attracting more researchers into this exciting and young area of research. It can be considered as the first book of its kind. The tools introduced and developed for the study of measure-valued processes in random environments can be used in a much broader area of nonlinear SPDEs.
An Introduction To Computational Stochastic Pdes
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Author : Gabriel J. Lord
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-11
An Introduction To Computational Stochastic Pdes written by Gabriel J. Lord and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-11 with Business & Economics categories.
This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
Probabilistic Theory Of Mean Field Games With Applications I
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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-01
Probabilistic Theory Of Mean Field Games With Applications I written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-01 with Mathematics categories.
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Probabilistic Theory Of Mean Field Games With Applications Ii
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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-08
Probabilistic Theory Of Mean Field Games With Applications Ii written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Mathematics categories.
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Partial Differential Equations For Probabalists Sic
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Author : Daniel W. Stroock
language : en
Publisher: Cambridge University Press
Release Date : 2008
Partial Differential Equations For Probabalists Sic written by Daniel W. Stroock and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Differential equations, Elliptic categories.
Kolmogorov's forward, basic results -- Non-elliptic regularity results -- Preliminary elliptic regularity results -- Nash theory -- Localization -- On a manifold -- Subelliptic estimates and Hörmander's theorem.
Pde Models For Multi Agent Phenomena
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Author : Pierre Cardaliaguet
language : en
Publisher: Springer
Release Date : 2018-12-22
Pde Models For Multi Agent Phenomena written by Pierre Cardaliaguet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-22 with Mathematics categories.
This volume covers selected topics addressed and discussed during the workshop “PDE models for multi-agent phenomena,” which was held in Rome, Italy, from November 28th to December 2nd, 2016. The content mainly focuses on kinetic equations and mean field games, which provide a solid framework for the description of multi-agent phenomena. The book includes original contributions on the theoretical and numerical study of the MFG system: the uniqueness issue and finite difference methods for the MFG system, MFG with state constraints, and application of MFG to market competition. The book also presents new contributions on the analysis and numerical approximation of the Fokker-Planck-Kolmogorov equations, the isotropic Landau model, the dynamical approach to the quantization problem and the asymptotic methods for fully nonlinear elliptic equations. Chiefly intended for researchers interested in the mathematical modeling of collective phenomena, the book provides an essential overview of recent advances in the field and outlines future research directions.