Basic stochastic processes基础随机过程

出版时间：2000-9  出版社：Springer Verlag  作者：Zdzislaw Brzezniak,Tomasz Zastawniak  页数：225  
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内容概要

　　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 Itô Stochastic Processes。 　　Provides a detailed treatment of conditional expectation & probability，a topic which is essential as a tool for stochastic processes。 Presented as a final year undergraduate text on stochastic processes，a tool used widely by statisticians　＆ researchers working in the mathematics of finance。 Softcover。 DLC： Stochastic processes。 　　This book is a final year undergraduate text on stochastic processes，a tool used widely by statisticians and researchers working，for example，in the mathematics of finance。 The book will give a detailed treatment of conditional expectation and probability，a topic which is essential as a tool for stochastic processes。 Although the book is a final year text，the authors have chosen to use exercises as the main means of explanation for the various topics，hence the course has a strong self-study element。 The authors have concentrated on major topics within stochastic analysis： martingales in discrete time and their convergence，Markov chains，stochastic processes in continuous time，with emphasis on the Poisson process and Brownian motion，as well as Ito stochastic calculus including stochastic differential equations。

书籍目录

1.Review of Probability　1.1  Events and Probability  1.2  Random Variables  1.3  Conditional Probability and Independence  1.4  Solutions2.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 a-Field  2.5  General Properties  2.6  Various Exercises on Conditional Expectation  2.7  Solutions3.Martingales in Discrete　3.1　Sequences of Random　3.2　Filtrations　3.3　Martingales　3.4　Games of Chance　3.5　Stopping Times　3.6　Optional Stopping Theorem　3.7　Solutions4.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  Solutions5.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 Markov Chains with Finite State　Space  5.5  Solutions6.Stochastic Processes in Continuous Time　6.1  General Notions  6.2  Poisson Process　　6.2.1  Exponential Distribution and Lack of Memory    6.2.2  Construction of the Poisson Process  　6.2.3  Poisson Process Starts from Scratch at Time t    6.2.4  Various Exercises on the Poisson Process　6.3  Brownian Motion　　6.3.1  Definition and Basic Properties    6.3.2  Increments of Brownian Motion    6.3.3  Sample Paths    6.3.4  Doob's Maximal L2 Inequality for Brownian Motion    6.3.5  Various Exercises on Brownian Motion　6.4  Solutions7.Ito Stochastic Calculus　7.1  It5 Stochastic Integral：Definition  7.2  Examples  7.3  Properties of the Stochastic Integral  7.4  Stochastic Differential and It6 Formula  7.5  Stochastic Differential Equations  7.6  SolutionsIndex