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# Basic stochastic processes : a course through exercises

Author: Zdzisław Brzeźniak; Tomasz Zastawniak London [u.a.] : Springer, 1999. Springer undergraduate mathematics series. Print book : English : 2nd print., with corrView all editions and formats 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  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Aufgabensammlung0 Gesamtdarstellung Internet resource Book, Internet Resource Zdzisław Brzeźniak; Tomasz Zastawniak Find more information about: Zdzisław Brzeźniak Tomasz Zastawniak 3540761756 9783540761754 246169050 x, 225 S : graph. Darst. 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 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 Markov Chains with Finite State Space.- 5.5 Solutions.- 6. 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 Solutions.- 7. Ito Stochastic Calculus.- 7.1 Ito Stochastic Integral: Definition.- 7.2 Examples.- 7.3 Properties of the Stochastic Integral.- 7.4 Stochastic Differential and Ito Formula.- 7.5 Stochastic Differential Equations.- 7.6 Solutions. Springer undergraduate mathematics series. Zdzisław Brzeźniak and Tomasz Zastawniak.

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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 Read more...

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