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Nonlinear Expectations and Stochastic Calculus under Uncertainty, Shige Peng


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Автор: Shige Peng
Название:  Nonlinear Expectations and Stochastic Calculus under Uncertainty
ISBN: 9783662599020
Издательство: Springer
Классификация:



ISBN-10: 3662599023
Обложка/Формат: Hardcover
Страницы: 212
Вес: 0.51 кг.
Дата издания: 2019
Серия: Probability Theory and Stochastic Modelling
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 10 illustrations, black and white; xiii, 212 p. 10 illus.
Размер: 234 x 156 x 14
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Подзаголовок: with Robust CLT and G-Brownian Motion
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author.This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes.With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter.Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.
Дополнительное описание: Sublinear Expectations and Risk Measures.- Law of Large Numbers and Central Limit Theorem under Uncertainty.- G-Brownian Motion and It?’s Calculus.- G-Martingales and Jensen’s Inequality.- Stochastic Differential Equations.- Capacity and Quasi-Surely Anal



Stochastic Calculus for Finance I

Автор: Shreve
Название: Stochastic Calculus for Finance I
ISBN: 0387401008 ISBN-13(EAN): 9780387401003
Издательство: Springer
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Цена: 8384.00 р.
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Описание: Developed for the professional Master`s program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several yearsExercises conclude every chapter;

Stochastic PDEs and Dynamics

Автор: Boling Guo, Hongjun Gao, Xueke Pu
Название: Stochastic PDEs and Dynamics
ISBN: 3110495104 ISBN-13(EAN): 9783110495102
Издательство: Walter de Gruyter
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Цена: 18586.00 р.
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Описание: This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: PreliminariesThe stochastic integral and It formulaOU processes and SDEsRandom attractorsApplicationsBibliographyIndex

Stochastic Analysis in Production Process and Ecology Under Uncertainty

Автор: Bogus?aw Bieda
Название: Stochastic Analysis in Production Process and Ecology Under Uncertainty
ISBN: 3642427804 ISBN-13(EAN): 9783642427800
Издательство: Springer
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Цена: 13059.00 р.
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Описание: Chapter five contains examples of using ecological Life Cycle Assessment (LCA) - a relatively new method of environmental impact assessment - which help in preparing pro-ecological strategy, and which can lead to reducing the amount of wastes produced in the ArcelorMittal Steel Plant production processes.

Shape Optimization under Uncertainty from a Stochastic Programming Point of View

Автор: Harald Held
Название: Shape Optimization under Uncertainty from a Stochastic Programming Point of View
ISBN: 3834809098 ISBN-13(EAN): 9783834809094
Издательство: Springer
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Цена: 14673.00 р.
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Описание: Optimization problems whose constraints involve partial differential equations (PDEs) are relevant in many areas of technical, industrial, and economic app- cations. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. The present text is among the ?rst in the research literature addressing stochastic uncertainty in the context of PDE constrained optimization. The focus is on shape optimization for elastic bodies under stochastic loading. Analogies to ?nite dim- sional two-stage stochastic programming drive the treatment, with shapes taking the role of nonanticipative decisions.The main results concern level set-based s- chastic shape optimization with gradient methods involving shape and topological derivatives. The special structure of the elasticity PDE enables the numerical - lution of stochastic shape optimization problems with an arbitrary number of s- narios without increasing the computational effort signi?cantly. Both risk neutral and risk averse models are investigated. This monograph is based on a doctoral dissertation prepared during 2004-2008 at the Chair of Discrete Mathematics and Optimization in the Department of Ma- ematics of the University of Duisburg-Essen. The work was supported by the Deutsche Forschungsgemeinschaft (DFG) within the Priority Program "Optimi- tion with Partial Differential Equations." Rudiger Schultz Acknowledgments I owe a great deal to my supervisors, colleagues, and friends who have always supported, encouraged, andenlightenedmethroughtheirownresearch, comments, and questions.

Elements of stochastic calculus and analysis

Автор: Stroock, Daniel W.
Название: Elements of stochastic calculus and analysis
ISBN: 3319770373 ISBN-13(EAN): 9783319770376
Издательство: Springer
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Цена: 7965.00 р.
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Описание: This book gives a somewhat unconventional introduction to stochastic analysis.

Nonlinear Mathematics for Uncertainty and its Applications

Автор: Shoumei Li; Xia Wang; Yoshiaki Okazaki; Jun Kawabe
Название: Nonlinear Mathematics for Uncertainty and its Applications
ISBN: 3662520389 ISBN-13(EAN): 9783662520383
Издательство: Springer
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Цена: 45712.00 р.
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Описание: From the content: Ordinal Preference Models Based on S-Integrals and Their Verification.- Strong Laws of Large Numbers for Bernoulli Experiments under Ambiguity.- Comparative Risk Aversion for g-Expected Utility Maximizers.- Riesz Type Integral Representations for Comonotonically Additive Functionals.- Pseudo-Concave Integrals.- On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts.- Upper Derivatives of Set Functions Represented as the Choquet Indefinite Integral.- On Regularity for Non-Additive Measure.

Nonlinear Stochastic Systems with Network-Induced Phenomena

Автор: Jun Hu; Zidong Wang; Huijun Gao
Название: Nonlinear Stochastic Systems with Network-Induced Phenomena
ISBN: 3319359290 ISBN-13(EAN): 9783319359298
Издательство: Springer
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Цена: 14365.00 р.
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Описание: Introduction.- Recursive Filtering for Time-Varying Nonlinear Systems with Stochastic Nonlinearities, Multiple Missing Measurements and Quantized Effects.- Recursive Filtering with Random Parameter Matrices, Multiple Fading Measurements, Probabilistic Sensor Delays, Correlated Noises and Gain-Constraint.- Probability-Guaranteed H-infinity Finite-Horizon Filtering for a Class of Nonlinear Time-Varying Systems with Sensor Saturations.- H-infinity Sliding-Mode Observer Design for a Class of Nonlinear Time-Delay Systems.- Robust Sliding-Mode Control for Uncertain Stochastic Systems with Time-Varying Delays, Randomly-Occurring Nonlinearities and Stochastic Nonlinearities.- Robust Sliding-Mode Control for Stochastic Systems with Randomly-Occurring Uncertainties, Randomly Occurring Nonlinearities, Mixed Time Delays and Markovian Jumping Parameters.- Conclusions and Future Work.

Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis

Автор: Gy?rgy Terdik
Название: Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis
ISBN: 0387988726 ISBN-13(EAN): 9780387988726
Издательство: Springer
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Цена: 14673.00 р.
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Описание: The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-Ito integrals and finally chaotic Wiener-Ito spectral representation of subordinated processes.

Nonlinear Filtering and Stochastic Control

Автор: S.K. Mitter; A. Moro
Название: Nonlinear Filtering and Stochastic Control
ISBN: 3540119760 ISBN-13(EAN): 9783540119760
Издательство: Springer
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Цена: 4884.00 р.
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Stochastic Nonlinear Systems in Physics, Chemistry, and Biology

Автор: L. Arnold; R. Lefever
Название: Stochastic Nonlinear Systems in Physics, Chemistry, and Biology
ISBN: 3642680402 ISBN-13(EAN): 9783642680403
Издательство: Springer
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Цена: 12577.00 р.
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Описание: The workshop brought some 25 physicists, chemists, and biologists - who deal with stochastic phenomena - and about an equal number of mathematicians - who are experts in the theory of stochastic processes - together.

Elementary Stochastic Calculus, with Finance in View

Автор: Mikosch, Thomas
Название: Elementary Stochastic Calculus, with Finance in View
ISBN: 9810235437 ISBN-13(EAN): 9789810235437
Издательство: World Scientific Publishing
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Цена: 7603.00 р.
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Описание: An elementary introduction to modelling with Ito integral or stochastic differential equations, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived.

Nonlinear Stochastic Systems with Incomplete Information

Автор: Bo Shen; Zidong Wang; Huisheng Shu
Название: Nonlinear Stochastic Systems with Incomplete Information
ISBN: 1447160002 ISBN-13(EAN): 9781447160007
Издательство: Springer
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Цена: 16977.00 р.
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Описание: Nonlinear Stochastic Processes shows the reader how to deal with the issue of network-induced incomplete information. It presents a unified framework for filtering and control problems in complex communication networks with limited bandwidth.


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