Stochastic calculus. An introduction through theory and exercises
type: Item
instance of: scholarly article
title: Stochastic calculus. An introduction through theory and exercises
zbMATH Open document ID: 1382.60001
DOI: 10.1007/978-3-319-62226-2
author: Yanyan Li
published in: Universitext
publication date: 2017-08-02T00:00:00Z
review text: The book presents some information from probability theory, followed by sections devoted to the main classes of stochastic processes, and completed by sections directly devoted to stochastic analysis. The first goal is to make the reader familiar with the basic elements of stochastic processes, such as Brownian motion, martingales and Markov processes and then move in the direction of stochastic integration. In general, the book consists of 13 chapters. Chapter 1 contains elements of probability, Chapters 2--3 introduce stochastic processes, especially, Brownian motion. Chapters 4 and 5 provide the main elements on conditioning, martingales and their applications. Chapter 6 is about Markov processes. From Chapter 7, stochastic calculus begins as such. Chapters 7 and 8 are concerned with stochastic integrals and Ito's formula. Chapter 9 investigates stochastic differential equations. Chapter 10 is about the relationship with PDEs. After the detour on numerical issues related to diffusion processes of Chapter 11, further notions of stochastic calculus, including Girsanov's theorem and representation theorems on martingales, are investigated in Chapter 12. The last chapter is devoted to financial applications. The book is written in clear language and in good style and will be useful for everybody who is interested in stochastic calculus; it is suited for beginners, students, researchers, teachers and practitioners.
Mathematics Subject Classification ID: 60-01
Mathematics Subject Classification ID: 60G05
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60Jxx
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 6755640
zbMATH Keywords: probability spaces
zbMATH Keywords: random variables
zbMATH Keywords: conditional probability
zbMATH Keywords: stochastic processes
zbMATH Keywords: Brownian motion
zbMATH Keywords: martingales
zbMATH Keywords: Markov processes
zbMATH Keywords: stochastic integration
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: partial differential equations and diffusions
zbMATH Keywords: simulation
zbMATH Keywords: Black-Scholes model
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-62226-2
OpenAlex ID: W4253749331
description: scientific article; zbMATH DE number 6755640