Advances In Nonlinear Partial Differential Equations And Stochastics
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Advances In Nonlinear Partial Differential Equations And Stochastics
Author | : Kawashima S,Yanagisawa Taku |
Publsiher | : World Scientific |
Total Pages | : 368 |
Release | : 1998-06-17 |
Genre | : Science |
ISBN | : 9789814496360 |
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In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Advances in Nonlinear Partial Differential Equations and Stochastics
Author | : Shuichi Kawashima,Taku Yanagisawa |
Publsiher | : World Scientific |
Total Pages | : 378 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9810233965 |
Download Advances in Nonlinear Partial Differential Equations and Stochastics Book in PDF, Epub and Kindle
In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Advances in Superprocesses and Nonlinear PDEs
Author | : Janos Englander,Brian Rider |
Publsiher | : Springer Science & Business Media |
Total Pages | : 129 |
Release | : 2013-03-21 |
Genre | : Mathematics |
ISBN | : 9781461462408 |
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Sergei Kuznetsov is one of the top experts on measure valued branching processes (also known as “superprocesses”) and their connection to nonlinear partial differential operators. His research interests range from stochastic processes and partial differential equations to mathematical statistics, time series analysis and statistical software; he has over 90 papers published in international research journals. His most well known contribution to probability theory is the "Kuznetsov-measure." A conference honoring his 60th birthday has been organized at Boulder, Colorado in the summer of 2010, with the participation of Sergei Kuznetsov’s mentor and major co-author, Eugene Dynkin. The conference focused on topics related to superprocesses, branching diffusions and nonlinear partial differential equations. In particular, connections to the so-called “Kuznetsov-measure” were emphasized. Leading experts in the field as well as young researchers contributed to the conference. The meeting was organized by J. Englander and B. Rider (U. of Colorado).
Stochastic Partial Differential Equations Second Edition
Author | : Pao-Liu Chow |
Publsiher | : CRC Press |
Total Pages | : 336 |
Release | : 2014-12-10 |
Genre | : Mathematics |
ISBN | : 9781466579552 |
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Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Lévy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of material. New to the Second Edition Two sections on the Lévy type of stochastic integrals and the related stochastic differential equations in finite dimensions Discussions of Poisson random fields and related stochastic integrals, the solution of a stochastic heat equation with Poisson noise, and mild solutions to linear and nonlinear parabolic equations with Poisson noises Two sections on linear and semilinear wave equations driven by the Poisson type of noises Treatment of the Poisson stochastic integral in a Hilbert space and mild solutions of stochastic evolutions with Poisson noises Revised proofs and new theorems, such as explosive solutions of stochastic reaction diffusion equations Additional applications of stochastic PDEs to population biology and finance Updated section on parabolic equations and related elliptic problems in Gauss–Sobolev spaces The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population growth model in a random environment, and a stochastic model in bond market theory. The author also explores the connection of stochastic PDEs to infinite-dimensional stochastic analysis.
Invariant Measures for Stochastic Nonlinear Schr dinger Equations
Author | : Jialin Hong,Xu Wang |
Publsiher | : Springer Nature |
Total Pages | : 220 |
Release | : 2019-08-22 |
Genre | : Mathematics |
ISBN | : 9789813290693 |
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This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.
Three Classes of Nonlinear Stochastic Partial Differential Equations
Author | : Jie Xiong |
Publsiher | : World Scientific |
Total Pages | : 177 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 9789814452366 |
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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.
Stochastic Differential and Difference Equations
Author | : Imre Csiszar,Gy. Michaletzky |
Publsiher | : Springer Science & Business Media |
Total Pages | : 358 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461219804 |
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Stochastic Partial Differential Equations and Applications
Author | : Giuseppe Da Prato,Luciano Tubaro |
Publsiher | : CRC Press |
Total Pages | : 480 |
Release | : 2002-04-05 |
Genre | : Mathematics |
ISBN | : 0203910176 |
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Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.