Name: Basic Stochastic Processes By Zdzislaw Brzezniak
SKU: 9783540761754
Price: 16.49 USD
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Basic Stochastic Processes Summary

Basic Stochastic Processes: A Course Through Exercises by Zdzislaw Brzezniak

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.

Basic Stochastic Processes Reviews

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

www.quantnotes.com

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.

Additional information

Sku

GOR002849694

ISBN 13

9783540761754

ISBN 10

3540761756

Title

Basic Stochastic Processes: A Course Through Exercises by Zdzislaw Brzezniak

Author

Zdzislaw Brzezniak

Series

Springer Undergraduate Mathematics Series

Condition

Used - Very Good

Binding type

Paperback

Publisher

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Year published

20000726

Number of pages

226

Prizes

N/A

Cover note

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us

Basic Stochastic Processes Zdzislaw Brzezniak

Basic Stochastic Processes by Zdzislaw Brzezniak

Summary

Basic Stochastic Processes Summary

Basic Stochastic Processes: A Course Through Exercises by Zdzislaw Brzezniak

Basic Stochastic Processes Reviews

Table of Contents

Additional information

Customer Reviews - Basic Stochastic Processes