Informal Introduction To Stochastic Calculus With Applications, An

by Ovidiu Calin

The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author aims to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.



A Few Introductory Problems
Basic Notions
Useful Stochastic Processes
Properties of Stochastic Processes
Stochastic Integration
Stochastic Differentiation
Stochastic Integration Techniques
Stochastic Differential Equations
Applications of Brownian Motion
Girsanov's Theorem and Brownian Motion
Some Applications of Stochastic Calculus
Hints and Solutions

Undergraduate and graduate students interested in stochastic processes.
Key
The book contains numerous problems with full solutions and plenty of worked out examples and figures, which facilitate material understanding
The material was tested on students at several universities around the world (Taiwan, Kuwait, USA); this led to a presentation form that balances both technicality and understanding
The presentation mimics as close as possible the same chapters as in deterministic calculus; former calculus students will find this chronology of ideas familiar to Calculus

Genres: Mathematics

314 pages, Kindle Edition

First published June 17, 2015

Reviews

[James Millikan · Rating 4 out of 5]

A solid introduction to the study of stochastic processes using the tools of calculus. The book doesn't presuppose a mastery of real analysis or measure theory, but does contain enough proofs to make a working knowledge of set theory and at least one previous course in higher mathematics strongly recommended. Some previous exposure to probability theory (discrete/continuous random variables, sigma-algebras, Kolmogorov's axioms, etc) would also be helpful.

One final word of warning: despite the title, the text is rather formal and the applied examples are rather few and far between. It's definitely a good introduction to Brownian motion, Ito calculus, Wiener processes, and stochastic differential equations, but don't expect a lot of immediate applied modeling examples. If you have an interest in pure mathematics, this is a good resource; if you are looking for more of an engineering-style text, perhaps look elsewhere.