Probability Models for DNA Sequence Evolution
How is genetic variability shaped by natural selection, demographic factors, and random genetic drift? To approach this question, we introduce and analyze a number of probability models beginning with the basics, and ending at the frontiers of current res
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Editors: J. Gani, C.C. Heyde, P. Jagers, T.G. Kurtz
Probability and Its Applications Anderson: Continuous-Time Markov Chains. Azencott/Dacunha-Castelle: Series of Irregular Observations. Bass: Diffusions and Elliptic Operators. Bass: Probabilistic Techniques in Analysis. Berglund/Gentz: Noise-Induced Phenomena in Slow-Fast Dynamical Systems. Biagini/Hu/Øksendal/Zhang: Stochastic Calculus for Fractional Brownian Motion and Applications. Chen: Eigenvalues, Inequalities and Ergodic Theory. Choi: ARMA Model Identification. Costa/Fragoso/Marques: Discrete-Time Markov Jump Linear Systems. Daley/Vere-Jones: An Introduction to the Theory of Point Processes Volume I: Elementary Theory and Methods, Second Edition. de la Pe˜na/Gin´e: Decoupling: From Dependence to Independence. Durrett: Probability Models for DNA Sequence Evolution, Second Edition. Galambos/Simonelli: Bonferroni-type Inequalities with Applications. Gani (ed): The Craft of Probabilistic Modelling. Grandell: Aspects of Risk Theory. Gut: Stopped Random Walks. Guyon: Random Fields on a Network. Kallenberg: Foundations of Modern Probability, Second Edition. Last/Brandt: Marked Point Processes on the Real Line. Leadbetter/Lindgren/Rootz´en: Extremes and Related Properties of Random Sequences and Processes. Molchanov: Theory of Random Sets. Nualart: The Malliavin Calculus and Related Topics. Rachev/R¨uschendorf: Mass Transportation Problems. Volume I: Theory. Rachev/R¨uschendorf: Mass Transportation Problems. Volume II: Applications. Resnick: Extreme Values, Regular Variation and Point Processes. Schmidli: Stochastic Control in Insurance. Shedler: Regeneration and Networks of Queues. Silvestrov: Limit Theorems for Randomly Stopped Stochastic Processes. Thorisson: Coupling, Stationarity and Regeneration. Todorovic: An Introduction to Stochastic Processes and Their Applications.
Richard Durrett
Probability Models for DNA Sequence Evolution Second Edition
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Richard Durrett Department of Mathematics Cornell University Ithaca, NY 14853-4201 USA
Series Editors J. Gani Stochastic Analysis Group, CMA Australian National University Canberra ACT 0200 Australia
C.C. Heyde Stochastic Analysis Group, CMA Australian National University Canberra ACT 0200 Australia
P. Jagers Mathematical Statistics Chalmers University of Technology SE-412 96 G¨oteberg Sweden
ISBN: 978-0-387-78168-6 DOI: 10.1007/978-0-387-78168-6
T.G. Kurtz Department of Mathematics University of Wisconsin 480 Lincoln Drive Madison, WI 53706 USA
e-ISBN: 978-0-387-78169-3
Library of Congress Control Number: 2008929756 c 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology no
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