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Applied Probability (Hardcover, 2nd ed. 2010)
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Applied Probability (Hardcover, 2nd ed. 2010)
Series: Springer Texts in Statistics
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Applied Probability presents a unique blend of theory and
applications, with special emphasis on mathematical modeling,
computational techniques, and examples from the biological
sciences. It can serve as a textbook for graduate students in
applied mathematics, biostatistics, computational biology, computer
science, physics, and statistics. Readers should have a working
knowledge of multivariate calculus, linear algebra, ordinary
differential equations, and elementary probability theory.
Chapter 1 reviews elementary probability and provides a brief
survey of relevant results from measure theory. Chapter 2 is an
extended essay on calculating expectations. Chapter 3 deals with
probabilistic applications of convexity, inequalities, and
optimization theory. Chapters 4 and 5 touch on combinatorics and
combinatorial optimization. Chapters 6 through 11 present core
material on stochastic processes. If supplemented with appropriate
sections from Chapters 1 and 2, there is sufficient material for a
traditional semester-long course in stochastic processes covering
the basics of Poisson processes, Markov chains, branching
processes, martingales, and diffusion processes. The second edition
adds two new chapters on asymptotic and numerical methods and an
appendix that separates some of the more delicate mathematical
theory from the steady flow of examples in the main text.
Besides the two new chapters, the second edition includes a more
extensive list of exercises, many additions to the exposition of
combinatorics, new material on rates of convergence to equilibrium
in reversible Markov chains, a discussion of basic reproduction
numbers in population modeling, and better coverage of Brownian
motion. Because many chapters are nearly self-contained,
mathematical scientists from a variety of backgrounds will find
Applied Probability useful as a reference
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