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Markov Processes, Brownian Motion, and Time Symmetry, Kai Lai Chung; John B. Walsh


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Автор: Kai Lai Chung; John B. Walsh
Название:  Markov Processes, Brownian Motion, and Time Symmetry
ISBN: 9781441919601
Издательство: Springer
Классификация: ISBN-10: 1441919600
Обложка/Формат: Paperback
Страницы: 432
Вес: 0.62 кг.
Дата издания: 19.11.2010
Серия: Grundlehren der mathematischen Wissenschaften
Язык: English
Размер: 234 x 156 x 23
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание:

From the reviews of the First Edition:

This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zurich, in the spring of 1970. The authors aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation. (Mathematical Reviews)

This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.



Brownian Motion and Stochastic Calculus

Автор: Karatzas
Название: Brownian Motion and Stochastic Calculus
ISBN: 0387976558 ISBN-13(EAN): 9780387976556
Издательство: Springer
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Цена: 46540.00 T
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Описание: This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of problems and exercises.

Exponential Functionals of Brownian Motion and Related Processes

Автор: Yor Marc
Название: Exponential Functionals of Brownian Motion and Related Processes
ISBN: 3540659439 ISBN-13(EAN): 9783540659433
Издательство: Springer
Цена: 65170.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume collects papers about the laws of geometric Brownian motions and their time-integrals, written by the author and coauthors between 1988 and 1998. These functionals play an important role in Mathematical Finance, as well as in (probabilistic) studies related to hyperbolic geometry, and also to random media. Throughout the volume, connections with more recent studies involving exponential functionals of LГ©vy processes are indicated. Some papers originally published in French are made available in English for the first time.

Brownian Motion: A Guide to Random Processes and Stochastic Calculus

Автор: Rene L. Schilling
Название: Brownian Motion: A Guide to Random Processes and Stochastic Calculus
ISBN: 3110741490 ISBN-13(EAN): 9783110741490
Издательство: Walter de Gruyter
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Цена: 64400.00 T
Наличие на складе: Нет в наличии.
Описание:

Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Ito Integrals'' and ''Brownian Local Times''.


Brownian Motion: An Introduction to Stochastic Processes

Автор: Rene L. Schilling, Lothar Partzsch
Название: Brownian Motion: An Introduction to Stochastic Processes
ISBN: 3110307294 ISBN-13(EAN): 9783110307290
Издательство: Walter de Gruyter
Цена: 42450.00 T
Наличие на складе: Нет в наличии.
Описание: Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.

Stochastic calculus for fractional brownian motion and related processes

Автор: Mishura, Yuliya
Название: Stochastic calculus for fractional brownian motion and related processes
ISBN: 3540758720 ISBN-13(EAN): 9783540758723
Издательство: Springer
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Цена: 53060.00 T
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Brownian Motion: A Guide to Random Processes and Stochastic Calculus

Автор: Schilling Renй L.
Название: Brownian Motion: A Guide to Random Processes and Stochastic Calculus
ISBN: 3110741253 ISBN-13(EAN): 9783110741254
Издательство: Walter de Gruyter
Рейтинг:
Цена: 65280.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:

Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itф Integrals'' and ''Brownian Local Times''.


Time Changes of the Brownian Motion: Poincare Inequality, Heat Kernel Estimate and Protodistance

Автор: Jun Kigami
Название: Time Changes of the Brownian Motion: Poincare Inequality, Heat Kernel Estimate and Protodistance
ISBN: 1470436205 ISBN-13(EAN): 9781470436209
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 67710.00 T
Наличие на складе: Нет в наличии.
Описание: In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including $n$-dimensional cube $[0, 1]^n$ are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on $[0, 1]^n$, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on $[0, 1]^2$ and self-similar measures.The author shows the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, he obtains diagonal lower and upper estimates of the heat kernel as time tends to $0$. In particular, to express the principal part of the lower diagonal heat kernel estimate, he introduces ``protodistance'' associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub-Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown.

Handbook of Brownian motion: facts and  formulae

Автор: A. N Borodin и P. Salminen
Название: Handbook of Brownian motion: facts and formulae
ISBN: 3034894627 ISBN-13(EAN): 9783034894623
Издательство: Springer
Цена: 121110.00 T
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Описание: There are two parts in this book. The first part is devoted mainly to the proper- ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re- lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style." By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications of diffusions and Brownian motion. In discussions with many of our colleagues we have found that they share this point of view. Our original plan included more things than we were able to realize. It turned out very soon when trying to put the plan into practice that the material would be too wide to be published under one cover. Excursion theory, which most of the recent results concerning linear Brownian motion and diffusions can be classified as, is only touched upon slightly here, not to mention Brownian motion in several dimensions which enters only through the discussion of Bessel processes. On the other hand, much attention is given to the theory of local time.

Fractional Brownian Motion: Approximations and Projections

Автор: Oksana Banna, Yuliya Mishura, Kostiantyn Ralchenko
Название: Fractional Brownian Motion: Approximations and Projections
ISBN: 1786302608 ISBN-13(EAN): 9781786302601
Издательство: Wiley
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Цена: 146730.00 T
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Описание:

This monograph studies the relationships between fractional Brownian motion (fBm) and other processes of more simple form. In particular, this book solves the problem of the projection of fBm onto the space of Gaussian martingales that can be represented as Wiener integrals with respect to a Wiener process. It is proved that there exists a unique martingale closest to fBm in the uniform integral norm. Numerical results concerning the approximation problem are given. The upper bounds of distances from fBm to the different subspaces of Gaussian martingales are evaluated and the numerical calculations are involved. The approximations of fBm by a uniformly convergent series of Lebesgue integrals, semimartingales and absolutely continuous processes are presented.

As auxiliary but interesting results, the bounds from below and from above for the coefficient appearing in the representation of fBm via the Wiener process are established and some new inequalities for Gamma functions, and even for trigonometric functions, are obtained.


Boundary Crossing of Brownian Motion

Автор: Hans R. Lerche
Название: Boundary Crossing of Brownian Motion
ISBN: 0387964339 ISBN-13(EAN): 9780387964331
Издательство: Springer
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Цена: 81050.00 T
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Описание: Two themes are treated which are closely related to each other and to the law of the iterated logarithm:* I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries.

Random Walks, Brownian Motion, and Interacting Particle Systems

Автор: H. Kesten; R. Durrett
Название: Random Walks, Brownian Motion, and Interacting Particle Systems
ISBN: 0817635092 ISBN-13(EAN): 9780817635091
Издательство: Springer
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Цена: 139750.00 T
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Описание: This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come.

Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion

Автор: Corinne Berzin; Alain Latour; Jos? R. Le?n
Название: Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion
ISBN: 3319078747 ISBN-13(EAN): 9783319078748
Издательство: Springer
Рейтинг:
Цена: 79190.00 T
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Описание: The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations.Concerning the proofs of the limit theorems, the "Fourth Moment Theorem" is systematically used, as it produces rapid and helpful proofs that can serve as models for the future.


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