General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions, Qi L?; Xu Zhang
Автор: Zhang, Jianfeng Название: Backward stochastic differential equations ISBN: 1493972545 ISBN-13(EAN): 9781493972548 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Preliminaries.- Part I The Basic Theory of SDEs and BSDEs.- Basics of Stochastic Calculus.- Stochastic Differential Equations.- Backward Stochastic Differential Equations.- Markov BSDEs and PDEs.- Part II Further Theory of BSDEs.- Reflected BSDEs.- BSDEs with Quadratic Growth in Z.- Forward Backward SDEs.- Part III The Fully Nonlinear Theory of BSDEs.- Stochastic Calculus Under Weak Formulation.- Nonlinear Expectation.- Path Dependent PDEs.- Second Order BSDEs.. Bibliography.- Index.
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: This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics.
Автор: Da Prato Название: Stochastic Equations in Infinite Dimensions ISBN: 1107055849 ISBN-13(EAN): 9781107055841 Издательство: Cambridge Academ Рейтинг: Цена: 21384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. Thoroughly updated, it also includes two brand new chapters surveying recent developments in the area.
Автор: N.V. Krylov; G. Da Prato; M. R?ckner; J. Zabczyk Название: Stochastic PDE`s and Kolmogorov Equations in Infinite Dimensions ISBN: 3540665455 ISBN-13(EAN): 9783540665458 Издательство: Springer Рейтинг: Цена: 5304.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables, connected with stochastic differential equations in finite or infinite dimensional spaces. These equations can be studied both by probabilistic and by analytic methods.
Автор: Gawarecki, Leszek Mandrekar, Vidyadhar Название: Stochastic differential equations in infinite dimensions ISBN: 3642266347 ISBN-13(EAN): 9783642266348 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume offers comprehensive coverage of modern techniques used for solving problems in infinite dimensional stochastic differential equations. It presents major methods, including compactness, coercivity, monotonicity, in different set-ups.
Introduction.- Stochastic Evolution Equations in Hilbert Spaces.- Optimal Strong Error Estimates for Galerkin Finite Element Methods.- A Short Review of the Malliavin Calculus in Hilbert Spaces.- A Malliavin Calculus Approach to Weak Convergence.- Numerical Experiments.- Some Useful Variations of Gronwall's Lemma.- Results on Semigroups and their Infinitesimal Generators.- A Generalized Version of Lebesgue's Theorem.- References.- Index.
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