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Springer Undergraduate Mathematics Ser.: Basic Stochastic Processes : A Course Through Exercises by Tomasz Zastawniak and Zdzislaw Brzezniak (1998, Trade Paperback)
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Basic Stochastic Processes : A Course Through Exercises, Paperback by Brzezniak, Zdzisaw; Zastawniak, Tomasz, ISBN 3540761756, ISBN-13 9783540761754, Brand New, Free shipping in the US Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. Th centers on exercises as the main means of explanation.
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About this product
Product Identifiers
PublisherSpringer London, The Limited
ISBN-103540761756
ISBN-139783540761754
eBay Product ID (ePID)825567
Product Key Features
Number of PagesX, 226 Pages
Publication NameBasic Stochastic Processes : a Course Through Exercises
LanguageEnglish
Publication Year1998
SubjectProbability & Statistics / Stochastic Processes, Probability & Statistics / General, Astronomy
TypeTextbook
Subject AreaMathematics, Science
AuthorTomasz Zastawniak, Zdzislaw Brzezniak
SeriesSpringer Undergraduate Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Height0.3 in
Item Weight30 Oz
Item Length9.3 in
Item Width7 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN98-007021
Dewey Edition21
ReviewsThis book fulfils its aim of providing good and interesting material for advanced undergraduate study. The Times Higher Education Supplement This is probably one of the best books to begin learning about the sometimes complex topic of stochastic calculus and stochastic processes from a more mathematical approach. Some literature are often accused of unnecessarily complicating the subject when applied to areas of finance. With this book you are allowed to explore the rigorous side of stochastic calculus, yet maintain a physical insight of what is going on. The authors have concentrated on the most important and useful topics that are encountered in common physical and financial systems www.quantnotes.com, This book fulfils its aim of providing good and interesting material for advanced undergraduate study. The Times Higher Education Supplement This is probably one of the best books to begin learning about the sometimes complex topic of stochastic calculus and stochastic processes from a more mathematical approach. Some literature are often accused of unnecessarily complicating the subject when applied to areas of finance. With this book you are allowed to explore the rigorous side of stochastic calculus, yet maintain a physical insight of what is going on. The authors have concentrated on the most important and useful topics that are encountered in common physical and financial systems www.quantnotes.com , This book fulfils its aim of providing good and interesting material for advanced undergraduate study.The Times Higher Education SupplementThis is probably one of the best books to begin learning about the sometimes complex topic of stochastic calculus and stochastic processes from a more mathematical approach. Some literature are often accused of unnecessarily complicating the subject when applied to areas of finance. With this book you are allowed to explore the rigorous side of stochastic calculus, yet maintain a physical insight of what is going on. The authors have concentrated on the most important and useful topics that are encountered in common physical and financial systemswww.quantnotes.com
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal519.2
Table Of Content1. Review of Probability.- 1.1 Events and Probability.- 1.2 Random Variables.- 1.3 Conditional Probability and Independence.- 1.4 Solutions.- 2. Conditional Expectation.- 2.1 Conditioning on an Event.- 2.2 Conditioning on a Discrete Random Variable.- 2.3 Conditioning on an Arbitrary Random Variable.- 2.4 Conditioning on a ?-Field.- 2.5 General Properties.- 2.6 Various Exercises on Conditional Expectation.- 2.7 Solutions.- 3. Martingales in Discrete.- 3.1 Sequences of Random Variables.- 3.2 Filtrations.- 3.3 Martingales.- 3.4 Games of Chance.- 3.5 Stopping Times.- 3.6 Optional Stopping Theorem.- 3.7 Solutions.- 4. Martingale Inequalities and Convergence.- 4.1 Doob's Martingale Inequalities.- 4.2 Doob's Martingale Convergence Theorem.- 4.3 Uniform Integrability and L1 Convergence of Martingales.- 4.4 Solutions.- 5. Markov Chains.- 5.1 First Examples and Definitions.- 5.2 Classification of States.- 5.3 Long-Time Behaviour of Markov Chains: General Case.- 5.4 Long-Time Behaviour of MarkovChains with Finite State Space.- 5.5 Solutions.- 6. Stochastic Processes in Continuous Time.- 6.1 General Notions.- 6.2 Poisson Process.- 6.3 Brownian Motion.- 6.4 Solutions.- 7. Itô Stochastic Calculus.- 7.1 Itô Stochastic Integral: Definition.- 7.2 Examples.- 7.3 Properties of the Stochastic Integral.- 7.4 Stochastic Differential and Itô Formula.- 7.5 Stochastic Differential Equations.- 7.6 Solutions.
SynopsisThis book has been designed for a final year undergraduate course in stochastic processes. It will also be suitable for mathematics undergraduates and others with interest in probability and stochastic processes, who wish to study on their own. The main prerequisite is probability theory: probability measures, random variables, expectation, independence, conditional probability, and the laws of large numbers. The only other prerequisite is calculus. This covers limits, series, the notion of continuity, differentiation and the Riemann integral. Familiarity with the Lebesgue integral would be a bonus. A certain level of fundamental mathematical experience, such as elementary set theory, is assumed implicitly. Throughout the book the exposition is interlaced with numerous exercises, which form an integral part of the course. Complete solutions are provided at the end of each chapter. Also, each exercise is accompanied by a hint to guide the reader in an informal manner. This feature willbe particularly useful for self-study and may be of help in tutorials. It also presents a challenge for the lecturer to involve the students as active participants in the course., This book has been designed for a final year undergraduate course in stochastic processes. It will also be suitable for mathematics undergraduates and others with interest in probability and stochastic processes, who wish to study on their own. The main prerequisite is probability theory: probability measures, random variables, expectation, independence, conditional probability, and the laws of large numbers. The only other prerequisite is calculus. This covers limits, series, the notion of continuity, differentiation and the Riemann integral. Familiarity with the Lebesgue integral would be a bonus. A certain level of fundamental mathematical experience, such as elementary set theory, is assumed implicitly. Throughout the book the exposition is interlaced with numerous exercises, which form an integral part of the course. Complete solutions are provided at the end of each chapter. Also, each exercise is accompanied by a hint to guide the reader in an informal manner. This feature will be particularly useful for self-study and may be of help in tutorials. It also presents a challenge for the lecturer to involve the students as active participants in the course., Stochastic processes is a tool widely used by statisticians and researchers working, for example, in the mathematics of finance. This is an introductory text that has a strong emphasis on exercises, complete with informal hints and fully-worked solutions.
LC Classification NumberQA273.A1-274.9
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