Probability Theory: An Advanced Course
Vivek S. Borkar
ISBN 10: 038794558X ISBN 13: 9780387945583
Editore: Springer-Verlag New York Inc., 1995
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New copy - Usually dispatched within 7-11 working days. Codice articolo B9780387945583
Riassunto:
This book is an advanced text on probability theory. By presupposing the background of a standard first course in real analysis and a 'soft' course in probability theory, it gives a compact treatment of several key topics in probability, selected on the basis of their importance in forming the foundations of the modern theory of stochastic processes. It is ideal for graduate students and researchers in probability theory and stochastic processes and their applications. It is also well suited for scientists in allied fields such as mathematical statistics/ economics/physics, electrical engineering, operations research who wish to augment their background in probability theory.
Contenuti: 1 Introduction.- 1.1 Random Variables.- 1.2 Monotone Class Theorems.- 1.3 Expectations and Uniform Integrability.- 1.4 Independence.- 1.5 Convergence Concepts.- 1.6 Additional Exercises.- 2 Spaces of Probability Measures.- 2.1 The Prohorov Topology.- 2.2 Skorohod’s Theorem.- 2.3 Compactness in P(S).- 2.4 Complete Metrics on P(S).- 2.5 Characteristic Functions.- 2.6 Additional Exercises.- 3 Conditioning and Martingales.- 3.1 Conditional Expectations.- 3.2 Martingales.- 3.3 Convergence Theorems.- 3.4 Martingale Inequalities.- 3.5 Additional Exercises.- 4 Basic Limit Theorems.- 4.1 Introduction.- 4.2 Strong Law of Large Numbers.- 4.3 Central Limit Theorem.- 4.4 The Law of Iterated Logarithms.- 4.5 Large Deviations.- 4.6 Tests for Convergence.- 4.7 Additional Exercises.- 5 Markov Chains.- 5.1 Construction and the Strong Markov Property.- 5.2 Classification of States.- 5.3 Stationary Distributions.- 5.4 Transient and Null Recurrent Chains.- 5.5 Additional Exercises.- 6 Foundations of Continuous-Time Processes.- 6.1 Introduction.- 6.2 Separability and Measurability.- 6.3 Continuous Versions.- 6.4 Cadlag Versions.- 6.5 Examples of Stochastic Processes.- 6.6 Additional Exercises.- References.
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Titolo: Probability Theory: An Advanced Course
Casa editrice: Springer-Verlag New York Inc.
Data di pubblicazione: 1995
Legatura: Paperback / softback
Condizione: New