TY - BOOK AU - Bhattacharya, Rabi AU - Waymire, Edward C. TI - Random walk, brownian motion, and martingales T2 - Graduate texts in mathematics, SN - 9783030789374 U1 - 519.21 PY - 2021/// CY - Switzerland PB - Springer Nature KW - Brownian motion processes KW - Random walk mathematics KW - Martingales mathematics KW - Branching processes mathematics KW - Markov property KW - Kolmogorov-Chentsov theorem KW - Navier-Stokes equations KW - Mathematical finance stochastic processes N1 - Includes bibliographical references and indexes N2 - 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 theorythroughout. 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 UR - https://link.springer.com/content/pdf/bfm:978-3-030-78939-8/1 UR - https://www.goodreads.com/book/show/59836040-random-walk-brownian-motion-and-martingales?from_search=true&from_srp=true&qid=IkxizONVbe&rank=1#CommunityReviews ER -