The longer a list of books is, the fewer will actually be referred to. The lists below have been kept short, in the hope that in this case less choice is more.

Probability and stochastic calculus books

1. • A first course in probability, Sheldon Ross, Macmillan (4th edition 1994, 420 pages)

2. • Probability and random processes, Geoffrey Grimmett and David Stirzaker, Oxford University Press (2nd edition 1992, 540 pages)

3. • Probability with martingales, David Williams, Cambridge University Press (1991, 250 pages)

4. • Continuous martingales and Brownian motion, Daniel Revuz and Mark Yor, Springer (2nd edition 1994, 550 pages)

5. • Diffusions, Markov processes, and martingales: vol. 2 Itô calculus, Chris Rogers and David Williams, Wiley (1987, 475 pages)

These books are arranged in increasing degrees of technicality and depth (with the last two being at an equivalent level) and contain the probabilistic material used in chapters one, two and three. Ross is an introduction to the basic (static) probabilistic ideas of events, likelihood, distribution and expectation. Grimmett and Stirzaker contain that material in their first half, as well as the development of random processes including some basic material on martingales and Brownian motion.

Probability with martingales not only lays the groundwork for integration, (conditional) expectation and measures, but also is an excellent introduction to martingales themselves. There is also a chapter containing a simple representation theorem and a discrete-time version of Black—Scholes.

Both Revuz and Yor, and Rogers and Williams provide a detailed technical coverage of stochastic calculus.