Monte Carlo Methods and Stochastic ProcessesEmmanuelGobetChapman & Hall/CRC, 2016, 310 pages, £44.99, hardcover ISBN: 978‐1‐498‐74622‐9
Year: 2018
Type: book-review
Abstract: Readership: Researchers in pure and applied probability, statistics and applied mathematics, who are interested in stochastic modelling.This book, initially originating from course notes, covers an exciting area at the intersection of stochastic processes and simulation-based methods.For an applied researcher seeking to understand a dynamic real-life system in engineering, natural sciences or biosciences, stochastic processes serve as a fundamental modelling instrument.However, the utility of the model depends on our ability to operationalise it, to equip ourselves with tools that inform the model from available data, to provide predictions of the system's behaviour and to extrapolate them into scenarios not yet observed.Often the classical apparatus of mathematics, probability theory and statistics fails to advance towards that goal as analytic, and even numerical solutions are notoriously difficult to develop for stochastic processes beyond a relatively small set of special cases.This book introduces the reader to the methodology that can push this envelope.The book starts with an overview of the history of the Monte-Carlo method followed by laying out a modern toolbox for stochastic simulations and general modelling of dependence used to describe multivariate vector-valued outcomes (Part A).Also included in this part are basic asymptotic results and variance reduction designs.At the core of the method, is the observation that partial differential equations emerging in the stochastic process theory are similar to the ones that describe heat or fluid dynamics in the natural sciences.This is presented in Part B via Brownian motion and related processes defined through stochastic differential equations.Monte-Carlo methods developed for solving partial differential equations are then brought to bear on the study of stochastic processes.Part C, the final part, is devoted to non-linear processes.It features backward stochastic differential equations and associated dynamic programming method, empirical regression and elements of approximation theory, and non-linear and interacting diffusion processes.The book is self-contained and supplies key facts from a typical advanced probability theory and statistics course in a set of appendices.While maintaining mathematical rigour, the book skillfully avoids complex mathematical issues such as measurability that often make the theory of stochastic processes inaccessible to applied researchers.The style of the book walks the fine line, which makes it an invaluable resource for scientists in pure and applied probability, statistics and applied mathematics, who are interested in stochastic modelling.Examples mostly come out of physics, but the comprehensive exposition of the method makes the book really valuable to any stochastic modeller.
Source: International Statistical Review
DOI: 10.1111/insr.12254
Author: Alexander Tsodikov
Institution: University of Michigan
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W2797757710