TAILIEUCHUNG - Basic Stochastic Processes: A Course Through Exercises

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,. | Springer Undergraduate Mathematics Series Springer London Berlin Heidelberg New York Barcelona Hong Kong Milan Paris Singapore . Iiiiiliininii Ivisory Board jfessor . Cameron Queen Mary and Westfield College . Chaplain University of Dundee K. Erdmann Oxford University jfessor . Rogers University of Bath E. Still Oxford University ifessor . Toland University of Bath her books in this series ic Linear Algebra . Blyth and . Robertson 3-540-76122-5 ments of Logic via Numbers and Sets . Johnson 3-540-76123-3 dtivariate Calculus and Geometry s. Dineen 3-540-76176-4 mentary Number Theory . Jones and . Jones 3-540-76197-7 ctor Calculus . Matthews 3-540-76180-2 roductory Mathematics Algebra and Analysis G. Smith 3-540-76178-0 roductory Mathematics Applications and Methods . Marshall 3-540-76179-9 jups Rings and Fields . Wallace 3-540-76177-2 iasure Integral and Probability M. Capinksi and E. Kopp 3-540-76260-4 I i i H 2 7 4- ư Zdzislaw Brzezniak and Tomasz Zastawniak Basic Stochastic Processes A Course Through Exercises With 21 Figures .

• Toán học
• Stochastic processes
• Poisson process
• stochastic calculus
• mathematics of finance
• Process Limits
• Stochastic Processes
• Queueing system
• nite number
• shop assistants
• a forming of queues
• Queueing systems
• without queues
• Some general types
• stochastic processes Download free ebooks at bookboon
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• Probability Examples c 9 – Stochastic Processes 2 © 2009 Leif Mejlbro & Ventus Publishing ApS ISBN 978 87 7681 525 7 Download free ebooks at bookboon
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• Stochastic Processes 2 Contents Contents Introduction 1 1
• 1 1
• 2 1
• 3 1
• 4 1
• 5 1
• 6 1
• 7 2 3 4 5 Theoretical background The Poisson process Birth and death processes Queueing theory in general Queueing system of innitely many shop assistants Queueing system of a nite number of shop assistants
• and with forming of queues Queueing systems with a nite number of shop assistants and without queues Some general types of stochastic processes The Poisson process Birth and death processes Queueing theory Other types of stochastic processes Index 5 6 6 8 11 11 12 15 17 19 37 52 117 126 The next step for top performing gradua
• Probability random variables and stochastic processes
• Probability random variables
• Probability variables
• Discrete time stochastic processes
• Markov chains
• Continuous time stochastic processes
• Itô’s lemma
• Stochastic integral
• Preliminaries
• Lecture Introduction to Stochastic Processes
• Introduction to Stochastic Processes
• Disjoint time intervals
• The stochastic process
• Homogeneous Poisson proces
• Markov chain
• Discrete parameter stochastic process
• Time homogeneous Markov chain
• Lecture Probability Theory
• Probability Theory
• Lý thuyết xác suất
• Stationary Stochastic Processes
• Systems with Stochastic Inputs
• Homogeneous poisson processes
• Holds trivially
• Probability density function
• Order statistics property
• Conditional distribution
• Theorem superposition
• Probability generating function
• Random variables
• Invariant measur
• Unique stationary distribution
• Symmetric transition probability matrix
• SLLN for Markov chains
• The long run proportion
• Dissection principle
• Limiting distribution
• Aperiodic Markov chain
• Stationary distribution
• Homogeneous Poisson process
• Discrete Markov chains
• Positive real numbers
• Heuristic justification
• Rigorous justification
• Positive random variables
• Exponential distribution
• Poissonian increments
• Inhomogeneous Poisson process
• Discrete parameter Markov chain
• Countable state space
• Mathematical description
• Transition probabilities
• Simple random walk
• On off process
• Random walks on groups
• Gambler's ruin problem
• Chapman Kolmogorov equation
• Decomposition of state space
• Deterministically monotone Markov chain
• Communication classes
• The dissection principle
• Non empty closed subsets
• Recurrent Markov chain
• E valued random variables
• Power series
• Abel's limit theorem
• Proof of the theorem