Basics of Applied Stochastic Processes

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes

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Editors: J. Gani, C.C. Heyde, P. Jagers, T.G. Kurtz



Probability and Its Applications Azencott et al.: Series of Irregular Observations. Forecasting and Model Building. 1986 Bass: Diffusions and Elliptic Operators. 1997 Bass: Probabilistic Techniques in Analysis. 1995 Berglund/Gentz: Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach. 2006 Biagini/Hu/Øksendal/Zhang: Stochastic Calculus for Fractional Brownian Motion and Applications. 2008 Chen: Eigenvalues, Inequalities and Ergodic Theory. 2005 Costa/Fragoso/Marques: Discrete-Time Markov Jump Linear Systems. 2005 Daley/Vere-Jones: An Introduction to the Theory of Point Processes I: Elementary Theory and Methods. 2nd ed. 2003, corr. 2nd printing 2005 Daley/Vere-Jones: An Introduction to the Theory of Point Processes II: General Theory and Structure. 2nd ed. 2008 de la Peña/Gine: Decoupling: From Dependence to Independence, Randomly Stopped Processes U-Statistics and Processes Martingales and Beyond. 1999 Del Moral: Feynman-Kac Formulae. Genealogical and Interacting Particle Systems with Applications. 2004 Durrett: Probability Models for DNA Sequence Evolution. 2002, 2nd ed. 2008 Galambos/Simonelli: Bonferroni-Type Inequalities with Equations. 1996 Gani (ed.): The Craft of Probabilistic Modelling. A Collection of Personal Accounts. 1986 Gut: Stopped Random Walks. Limit Theorems and Applications. 1987 Guyon: Random Fields on a Network. Modeling, Statistics and Applications. 1995 Kallenberg: Foundations of Modern Probability. 1997, 2nd ed. 2002 Kallenberg: Probabilistic Symmetries and Invariance Principles. 2005 Lai/de la Peña/Shao: Self-Normalized Processes. Limit Theory and Statistical Applications. 2009 Last/Brandt: Marked Point Processes on the Real Line. 1995 Molchanov: Theory of Random Sets. 2005 Nualart: The Malliavin Calculus and Related Topics, 1995, 2nd ed. 2006 Rachev/Rueschendorf: Mass Transportation Problems. Volume I: Theory and Volume II: Applications. 1998 Resnick: Extreme Values, Regular Variation and Point Processes. 1987 Schmidli: Stochastic Control in Insurance. 2008 Schneider/Weil: Stochastic and Integral Geometry. 2008 Serfozo: Basics of Applied Stochastic Processes. 2009 Shedler: Regeneration and Networks of Queues. 1986 Silvestrov: Limit Theorems for Randomly Stopped Stochastic Processes. 2004 Thorisson: Coupling, Stationarity and Regeneration. 2000 •

Richard Serfozo

Basics of Applied Stochastic Processes

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Richard Serfozo

Georgia Institute of Technology School of Industrial & Systems Engineering 765 Ferst Drive NW., Atlanta GA 30332-0205 USA [email protected]

Series Editors: Joe Gani Chris Heyde

Thomas G. Kurtz

Centre for Mathematics and its Applications Mathematical Sciences Institute Australian National University Canberra, ACT 0200 Australia [email protected]

Department of Mathematics University of Wisconsin - Madison 480 Lincoln Drive Madison, WI 53706-1388 USA [email protected]

Peter Jagers Mathematical Statistics Chalmers University of Technology and Göteborg (Gothenburg) Univers