An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L
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An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L
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Author : Nikos Katzourakis
language : en
Publisher: Springer
Release Date : 2014-11-26
An Introduction To Viscosity Solutions For Fully Nonlinear Pde With Applications To Calculus Of Variations In L written by Nikos Katzourakis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-26 with Mathematics categories.
The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.
Variational Inequalities In Management Science And Finance
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Author : Andrianos E. Tsekrekos
language : en
Publisher: Springer Nature
Release Date : 2024-12-20
Variational Inequalities In Management Science And Finance written by Andrianos E. Tsekrekos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-20 with Business & Economics categories.
This book provides a rigorous introduction to the theory, computation, and applications of variational inequalities (VIs), with a focus on applications in management science and finance. It aims to bridge the gap between the abstract mathematical treatments of the subject and simplistic, non-rigorous approaches often used in financial economics or managerial literature. Building on fundamental examples of concrete applications drawn from management science and finance, the book gradually develops the connection between optimal stopping problems and variational inequalities. It provides precise results on their derivation, solution properties, and their use to derive optimal policies in general frameworks of stochastic factors driving the state processes. Emphasis is also placed on the numerical treatment and approximation of VIs. All technical results are illustrated in detail for the characteristic problems presented at the beginning as motivating examples. It also offers a brief introduction to more advanced topics, including VIs for multi-scale problems and VIs related to optimal stopping problems under model uncertainty. This book will be of interest to graduate students and researchers who wish for a quick, yet thorough introduction to the field. Practitioners who want to familiarise themselves with applications of VIs in management science and finance will also find this book useful.
Game Theory And Partial Differential Equations
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Author : Pablo Blanc
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-07-22
Game Theory And Partial Differential Equations written by Pablo Blanc and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-22 with Mathematics categories.
Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.
An Illustrative Introduction To Modern Analysis
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Author : Nikolaos Katzourakis
language : en
Publisher: CRC Press
Release Date : 2018-01-02
An Illustrative Introduction To Modern Analysis written by Nikolaos Katzourakis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Mathematics categories.
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.
Notes On Tug Of War Games And The P Laplace Equation
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Author : Mikko Parviainen
language : en
Publisher: Springer Nature
Release Date : 2024-02-22
Notes On Tug Of War Games And The P Laplace Equation written by Mikko Parviainen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-22 with Mathematics categories.
This book addresses the interplay between stochastic processes and partial differential equations. More specifically, it focuses on the connection between the nonlinear p-Laplace equation and the stochastic game called tug-of-war with noise. The connection in this context was discovered approximately 15 years ago and has since provided new insights and approaches. These lecture notes provide a brief but detailed and accessible introduction to the subject and to the more research-oriented literature. The book also presents the parabolic case side by side with the elliptic case, highlighting the fact that elliptic and parabolic equations are close in spirit in certain aspects. Moreover, it covers some parts of the regularity theory for these problems. Graduate students and advanced undergraduate students with a basic understanding of probability and partial differential equations will find this book useful.
Siam Journal On Control And Optimization
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Author : Society for Industrial and Applied Mathematics
language : en
Publisher:
Release Date : 2008
Siam Journal On Control And Optimization written by Society for Industrial and Applied Mathematics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Control theory categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Enciclopedia Italiana Di Scienze Lettere Ed Arti Quinta Appendice 1979 1992 5 V 6 Appendice 2000 Pt 1 A La Pt 2 Le Z Pt 3 Indici 1929 2000 A K Pt 4 L Z Pt 5 Eredit Del Novecento
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Author : Giovanni Gentile
language : it
Publisher:
Release Date : 1992
Enciclopedia Italiana Di Scienze Lettere Ed Arti Quinta Appendice 1979 1992 5 V 6 Appendice 2000 Pt 1 A La Pt 2 Le Z Pt 3 Indici 1929 2000 A K Pt 4 L Z Pt 5 Eredit Del Novecento written by Giovanni Gentile and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Encyclopedias and dictionaries, Italian categories.
Viscosity Solutions And Applications
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Author : Martino Bardi
language : en
Publisher: Springer
Release Date : 2006-11-13
Viscosity Solutions And Applications written by Martino Bardi 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 volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes.
Numerical Methods For Viscosity Solutions And Applications
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Author : Maurizio Falcone
language : en
Publisher: World Scientific
Release Date : 2001
Numerical Methods For Viscosity Solutions And Applications written by Maurizio Falcone and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume can attract readers involved in the numerical approximation of differential models in the above-mentioned fields of applications, engineers, graduate students as well as researchers in numerical analysis.