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 11present 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, manyadditions 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 froma variety of backgrounds will find Applied Probability useful as a reference Comprehensive coverage of Applied Probability Emphasis on concrete calculations and computational methods Clarity of writing and mathematical explanation INDICE: Basic Notions of Probability Theory.- Calculation of Expectations.- Convexity, Optimization, and Inequalities.- Combinatorics.- Combinatorial Optimization.- Poisson Processes.- Discrete-Time Markov Chains.- Continuous-TimeMarkov Chains.- Branching Processes.- Martingales.- Diffusion Processes.- Asymptotic Methods.- Numerical Methods.- Poisson Approximation.- Number Theory.
- ISBN: 978-1-4419-7164-7
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 436
- Fecha Publicación: 29/08/2010
- Nº Volúmenes: 1
- Idioma: Inglés