A Weak Convergence Approach to the Theory of Large Deviations

Передня обкладинка
John Wiley & Sons, 27 лют. 1997 р. - 504 стор.
Applies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach

The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems.

Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.
 

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Зміст

Formulation of Large Deviation Theory in Terms of the Laplace
1
Laplace Principle for the Random Walk Model with Continuous
148
Laplace Principle for the Empirical Measures of a Markov Chain
275
Extensions of the Laplace Principle for the Empirical Measures
320
Laplace Principle for ContinuousTime Markov Processes with
350
Bibliography
458
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Про автора (1997)

PAUL DUPUIS is a professor in the Division of Applied Mathematics at Brown University in Providence, Rhode Island.

RICHARD S. ELLIS is a professor in the Department of Mathematics and Statistics at the University of Massachusetts at Amherst.

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