Probability and Random ProcessesThis completely revised text provides a simple but rigorous introduction to probability. It discusses a wide range of random processes in some depth with many examples, and gives the beginner some flavor of more advanced work, by suitable choice of material. The book begins with basic material commonly covered in first-year undergraduate mathematics and statistics courses, and finishes with topics found in graduate courses. Important features of this edition include new and expanded sections in the early chapters, providing more illustrative examples and introducing more ideas early on; two new chapters providing more comprehensive treatment of the simpler properties of martingales and diffusion processes; and more exercises at the ends of almost all sections, with many new problems at the ends of chapters. The companion volume Probability and Random Processes: Problems and Solutions includes complete worked solutions to all exercises and problems of this edition. This proven text will be useful for mathematics and natural science undergraduates at all levels, and as a reference book for graduates and all those interested in the applications of probability theory. |
Common terms and phrases
a₁ arrival autocovariance function birth-death process branching process calculate called characteristic function conditional expectation continuous continuous-time convergence countable deduce defined Definition discrete-time distributed random variables distribution function distribution with parameter equation ergodic event Example Exercises exists exponentially distributed function F given Hence identically distributed random independent identically distributed independent random variables inequality interarrival interval irreducible large numbers Lemma Let X1 Markov chain Markov property martingale martingale with respect mass function non-negative o-field obtain P₁ particle Poisson process probability generating function probability space Problem process with intensity Proof prove queue random walk real numbers renewal process result S₁ sample paths satisfies Section sequence Show stationary distribution stationary process strongly stationary submartingale subsets Suppose T₁ taking values theorem theory tosses variance vector Wiener process X₁ X₂ Y₁ Y₂ Z₁ zero means