Description: Basic Stochastic Processes by Tomasz Zastawniak, Zdzislaw Brzezniak 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description This book is a final year undergraduate text on stochastic processes, a tool used widely by statisticians and researchers working in the mathematics of finance. The book will give a detailed treatment of conditional expectation and probability, a topic which in principle belongs to probability theory, but is essential as a tool for stochastic processes. Although the book is a final year text, the author has chosen to use exercises as the main means of explanation for the various topics, and the book will have a strong self-study element. The author has concentrated on the major topics within stochastic analysis: Stochastic Processes, Markov Chains, Spectral Theory, Renewal Theory, Martingales and Ito Stochastic Processes. Author Biography Zastawniak of the University of Hull, UK Table of Contents 1. 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 Doobs Martingale Inequalities.- 4.2 Doobs 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. Review 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 Promotional Springer Book Archives Long Description 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. Review Text 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 Review Quote 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 systems Feature Informal hints and fully worked solutions accompanying the exercises Strong emphasis on self-study Description for Sales People Stochastic processes is a tool widely used by statisticians andresearchers working, for example, in the mathematics of finance. This isan introductory text that has a strong emphasis on exercises, completewith informal hints and fully-worked solutions. Details ISBN3540761756 Author Zdzislaw Brzezniak Short Title BASIC STOCHASTIC PROCESSES 199 Language English ISBN-10 3540761756 ISBN-13 9783540761754 Media Book Format Paperback DEWEY 519.2 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Subtitle A Course Through Exercises Place of Publication Berlin Country of Publication Germany Birth 1959 Edition 1st Pages 226 DOI 10.1007/b60907;10.1007/978-1-4471-0533-6 UK Release Date 2000-07-26 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 1st ed. 1999. Corr. 3rd printing 2000 Series Springer Undergraduate Mathematics Series Illustrations X, 226 p. Audience Undergraduate Year 1998 Publication Date 1998-10-16 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96257072;
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ISBN-13: 9783540761754
Book Title: Basic Stochastic Processes
Number of Pages: 226 Pages
Publication Name: Basic Stochastic Processes: a Course Through Exercises
Language: English
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Item Height: 235 mm
Subject: Mathematics, Astronomy
Publication Year: 2000
Type: Textbook
Item Weight: 850 g
Author: Zdzislaw Brzezniak, Tomasz Zastawniak
Item Width: 178 mm
Format: Paperback
