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Titlebook: Random Walk, Brownian Motion, and Martingales; Rabi Bhattacharya,Edward C. Waymire Textbook 2021 Springer Nature Switzerland AG 2021 Stoch

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书目名称Random Walk, Brownian Motion, and Martingales
编辑Rabi Bhattacharya,Edward C. Waymire
视频video
概述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
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Random Walk, Brownian Motion, and Martingales;  Rabi Bhattacharya,Edward C. Waymire Textbook 2021 Springer Nature Switzerland AG 2021 Stoch
描述.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
出版日期Textbook 2021
关键词Stochastic processes textbook; Random walk mathematics; Branching processes mathematics; Martingales ma
版次1
doihttps://doi.org/10.1007/978-3-030-78939-8
isbn_ebook978-3-030-78939-8Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer Nature Switzerland AG 2021
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Continuous Parameter Martingales,In this chapter some of the main theorems for discrete parameter martingales obtained in previous chapters are extended to continuous parameter martingales. A central point is the use of martingale theory for the regularization of sample paths of stochastic processes.
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First Passage Time Distributions for Brownian Motion with Drift and a Local Limit Theorem,A local limit theorem for convergence of probability density functions is provided as a tool for the computation of hitting time distributions for Brownian motion, with or without drift, as a limit of hitting times for random walk, and other asymptotic limit theorems of this nature.
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