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Field name	Details
Dewey Class	519.2
Title	Basic Stochastic Processes ([EBook] :) : A Course Through Exercises / by Zdzisław Brzeźniak, Tomasz Zastawniak.
Author	Brzeźniak, Zdzisław
Added Personal Name	Zastawniak, Tomasz
Other name(s)	SpringerLink (Online service)
Publication	London : Springer, London , 1999.
Physical Details	X, 226 pages : online resource.
Series	Springer undergraduate mathematics series 1615-2085
ISBN	9781447105336
Summary Note	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.:
Contents note	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 -- 6.3 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4471-0533-6
Links to Related Works	Subject References: Astronomy . Astronomy, Observations and Techniques . Observations, Astronomical . Probabilities . Probability theory and stochastic processes . Authors: author . Brzeźniak, Zdzisław . Zastawniak, Tomasz . Corporate Authors: SpringerLink (Online service) . Series: Springer undergraduate mathematics series . Classification: 519.2 .

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Basic Stochastic Processes: A Course Through Exercises

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