Stochastic differential equations

By: Evans, C. LawrenceMaterial type: TextTextPublication details: Providence, RI: American Mathematical Society, [c]2017ISBN: 9781470437343Subject(s): MathematicsDDC classification: QA274.23
Contents:
1. Introduction 2. A crash course in probability theory 3. Brownian motion and "white noise" 4. Stochastic integrals 5. Stochastic differential equations 6. Applications
Summary: This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive "white noise" and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Itô stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book)."-- Provided by publisher
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Book Book ICTS
Mathematic Rack No 5 QA274.23 (Browse shelf (Opens below)) Available Billno:IN 003 582; Billdate: 2018-01-11 00880

1. Introduction
2. A crash course in probability theory
3. Brownian motion and "white noise"
4. Stochastic integrals
5. Stochastic differential equations
6. Applications

This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive "white noise" and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Itô stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book)."-- Provided by publisher