Stability of Infinite Dimensional Stochastic Differential Equations with Applications, Liu, Kai
Автор: Oksendal Название: Stochastic Differential Equations ISBN: 3540047581 ISBN-13(EAN): 9783540047582 Издательство: Springer Рейтинг: Цена: 8223.00 р. Наличие на складе: Есть (1 шт.) Описание: Gives an introduction to the basic theory of stochastic calculus and its applications. This book offers examples in order to motivate and illustrate the theory and show its importance for many applications in for example economics, biology and physics.
Описание: This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces.The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use.This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.
Описание: Preface.- Notations and Abbreviations.- Introduction and Motivating Examples.- Mathematical machinery.- Yosida Approximations of Stochastic Differential Equations.- Yosida Approximations of Stochastic Differential Equations with Jumps.- Applications to Stochastic Stability.- Applications to Stochastic Optimal Control.- Appendix A: Nuclear and Hilbert-Schmidt Operators.- Appendix B: Multivalued Maps.- Appendix C: Maximal Monotone Operators.- Appendix D: The Duality Mapping.- Appendix E: Random Multivalued Operators.- Bibliographical Notes and Remarks.- Bibliography.
Автор: R. M. M. Mattheij Название: Partial Differential Equations ISBN: 0898715946 ISBN-13(EAN): 9780898715941 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 21318.00 р. Наличие на складе: Нет в наличии.
Описание: Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.
Описание: This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the approach.The book is written for mathematicians who work in the field of partial differential and integral equations, physicists and engineers dealing with computational methods and applied probability, for students and postgraduates studying mathematical physics and numerical mathematics. Contents: IntroductionRandom walk algorithms for solving integral equationsRandom walk-on-boundary algorithms for the Laplace equationWalk-on-boundary algorithms for the heat equationSpatial problems of elasticityVariants of the random walk on boundary for solving stationary potential problemsSplitting and survival probabilities in random walk methods and applicationsA random WOS-based KMC method for electron-hole recombinationsMonte Carlo methods for computing macromolecules properties and solving related problemsBibliography
Автор: Coron Jean-Michel, Li Ta-Tsien, Li Yachun Название: One-Dimensional Hyperbolic Conservation Laws and Their Applications ISBN: 9813276177 ISBN-13(EAN): 9789813276178 Издательство: World Scientific Publishing Рейтинг: Цена: 20592.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.
Автор: Giuseppe Da Prato; Luciano Tubaro Название: Stochastic Partial Differential Equations and Applications II ISBN: 3540515100 ISBN-13(EAN): 9783540515104 Издательство: Springer Рейтинг: Цена: 4884.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Boris L. Rozovskii; Richard B. Sowers Название: Stochastic Partial Differential Equations and Their Applications ISBN: 3540552928 ISBN-13(EAN): 9783540552925 Издательство: Springer Рейтинг: Цена: 12157.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main topics for discussion at the confe-rence were: non-linear SPDE`s and Markov property for randomfields, modern stochastic calculuses, numerical and asympto-tic methods for SPDE`s, applications of SPDE`s with emphasisonnon-linear filtering, stochastic control and statisticalfluid dynamics.
Описание: This book will help make backward stochastic differential equations (BSDEs) more accessible to those interested in applying these equations to actuarial and financial problems.
Описание: In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems.
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