Basic Stochastic Processes

Rating:
Summary: Only for Math majors
Review: I am giving this book two stars based on its usefulness for me. I am wading through the book now, and it's going very slowly.

I made the mistake of equating teaching stochastic processes through exercises as meaning that those exercises were application oriented. It turns out that there is very little application in the book at all, so I am having a hard time with it.

I just wanted to warn other business academics (and non-mathematicians in general) who might be tempted to make the foray into stochastic processes by way of this book. Despite brief opening remarks in each chapter about where these concepts might be applied, you're pretty much left on your own to imagine how. Plus, you need to realize that it's written for someone who came up through the ranks as a mathematician, not a (albeit quantitatively oriented) business scholar.

Rating:
Summary: An excellent starter book : pre-SDEs
Review: I've worked through this book. It's an excellent introduction
to stochastic processes, sigma-algebras and quite an
expanded introduction to conditional expectation.
This nicely expands conditioning on an event, to conditioning
on (in order) a discrete rv, a continuous rv, a sigma-algebra
generated by a rv, and finally to just a sigma-algebra.
Only the Martingale Inequalities chapter seems a bit
isolated but is of course used later.

This book is Chap 2 of Oksendal (Mathematical Preliminaries).
For a PhD in maths/mathematical finance this is maybe a week
or twos work. It looks like a terms course for undergrads.

Rating:
Summary: Great Mid-Level Intro
Review: This book fills the gap between the too basic and quite advanced accounts of stochastic calculus. Great for someone with solid--but not graduate level--math background.

Rating:
Summary: Stochastic Processes
Review: This is an excellent book for anyone who can use maths at degree level. Forget complex analysis, this is far and away the best book for a good subject...

JH