|Item type||Current location||Call number||Status||Date due||Barcode|
|Books||519.282 BHA (Browse shelf)||Available||034168|
|519.27 BOL Mathematics of the big four casino table games : blackjack, baccarat, craps, and roulette||519.27 BOL Mathematics of casino carnival games||519.27 ETH Doctrine of chances : probabilistic aspects of gambling||519.282 BHA Random walk, Brownian motion, and martingales||519.282 GEN Random number generation and Monte Carlo methods||519.282 RUD Elements of the random walk : an introduction for advanced students and researchers||519.282 SOB Primer for the Monte Carlo method|
Includes bibliographical references and indexes.
This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov-Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.