Random walk, brownian motion, and martingales
Bhattacharya, Rabi
Random walk, brownian motion, and martingales - Switzerland : Springer Nature, 2021. - xv, 396p. - Graduate texts in mathematics, 292. 2197-5612 ; .
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 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
9783030789374
Brownian motion processes.
Random walk mathematics
Martingales mathematics
Branching processes mathematics
Markov property
Kolmogorov-Chentsov theorem
Navier-Stokes equations
Mathematical finance stochastic processes
519.21 / BHA-R
Random walk, brownian motion, and martingales - Switzerland : Springer Nature, 2021. - xv, 396p. - Graduate texts in mathematics, 292. 2197-5612 ; .
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 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
9783030789374
Brownian motion processes.
Random walk mathematics
Martingales mathematics
Branching processes mathematics
Markov property
Kolmogorov-Chentsov theorem
Navier-Stokes equations
Mathematical finance stochastic processes
519.21 / BHA-R
