Basic stochastic processes基础随机过程

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

作者简介

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. The book centers on exercises as the main means of explanation.

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