Probability and Random ProcessesThis recent textbook on elementary probability and random processes isnow reprinted. There are three main aims : to provide a simple but rigorous induction toprobability without exposing the reader to overmuch measure theory, todiscuss a wide range of random processes in some depth with manyexamples, and to give the beginner some flavour of more advanced work,by suitable choice of material. The book begins with basic material commonly covered in first. yearundergraduates mathematics and statistics courses, and finishes , withtopics to be found in graduate courses. Besides the large numbers ofexamples worked in the text there are more than two hundred problems tobe worked by the student. An appendix includes solutions and hints forselected problems. The book should therefore be useful as a text formathematics and natural science undergraduates at all levels from first tofinal-year degree work, and useful as a reference book for graduates and allthose interested in the applications of probability theory. The first five chapters de al with basic probability, including simpleproperties of random variables and their distributions, conditioning and expectation, weak laws of large numbers and the central limittheorem, with elementary discussions of random walks and branching processes. There follow straightforward presentations ofMarkov chains in discrete and continuous time, and the convergence of random variables leading to the strong law of large numbersand martingales. The book concludes with chapters on main stream applications of probability: stationary processes, diffusionprocesses, renewal processes, and queuing processes. The excellent early reviews include the following praise for this achievement: Although it competes with a very large number of otherbooks on similar topics, this new textbook on probability and stochastic processes should quickly become established as one of thebest texts available at undergraduate or MSc level. Valerie Isham in The Times Higher Education Supplement. I believe this book will be most valuable to postgraduates and research workers in mathematics and statistics needing a quick butthorough introduction to probability and to advanced undergraduates specialising in probability. R. L. Smith in the Bulletin of theLondon Mathematical Society. |
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A₁ arrival asserts asymptotic autocovariance function B₁ branching process called characteristic function conditional expectation continuous continuous-time convergence in distribution countable deduce defined Definition denote dF(x discrete-time distributed with parameter distribution function equation ergodic event Example exists exponentially distributed finite function F Fx(x given holds independent identically distributed independent variables inequality integral inter-arrival interval irreducible joint density function Large Numbers Law of Large Lemma Let X1 Markov chain Markov property martingale mass function N₁ non-negative non-null persistent notation obtain P₁ particle Poisson process probability space Problem Proof random variables random walk real numbers renewal process result S₁ sample paths satisfies Section sequence solution spectral stationary distribution stationary process Strong Law strongly stationary subsets suppose T₁ taking values tion transient variance Wiener process X₁ Y₁ Z₁