Random Walk, Brownian Motion, and Martingales
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Beschreibung
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.
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.
Offers an accessible introduction to the rigorous study of stochastic processes Builds from simple examples to formal proofs, illuminating key ideas and computations Showcases a selection of important contemporary applications, including mathematical finance, optimal stopping, and ruin theory
Autor*in
Rabi Bhattacharya
Themen in »Random Walk, Brownian Motion, and Martingales«
Stochastic processes textbook Random walk mathematics Branching processes mathematics Martingales mathematics Brownian motion textbook Poisson processes Kolmogorov-Chentsov theorem Markov property strong Markov property Simple random walk Renewal theory mathematics Mathematical finance stochastic processes Optimal stopping Branching random walk Navier-Stokes equations
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“The present text does an outstanding job of presenting many complementary aspects of the subject in a unified and coherent way … the subject matter and appreciation for the work of the authors in producing such an engaging and readable book. The authors suggest various models for graduate-level courses … . There is a great deal in the book that will be interesting, stimulating, and enjoyable for readers with an interest in probability theory and stochiastic processes.” (Andrew Wade, zbMATH 1489.60001, 2022)
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