How about grimmett & stirzaker: probability & random processes
New sections on Markov chain Monte Carlo, coupling and its applications, geometrical probability, spatial Poisson processes, Stochastic calculus and the Itô integral, Itô's formula and applications (including the Black-Scholes formula), networks of queues, and renewal-reward theorems and applications.
A separate volume including worked solutions to the problems and exercises will be available.
Minimal prerequisites (basic algebra and calculus)
The third edition of this successful text gives a rigorous introduction to probability theory and the discussion of the most important random processes in some depth. It includes various topics which are suitable for undergraduate courses, but are not routinely taught. It is suitable to the beginner, and provides a taste and encouragement for more advanced work. There are four main aims: 1) to provide a thorough but straightforward account of basic probability, giving the reader a natural feel for the subject unburdened by oppressive technicalities, 2) to discuss important random processes in depth with many examples. 3) to cover a range of important but less routine topics, 4) to impart to the beginner the flavour of more advanced work. The books begins with basic ideas common to many undergraduate courses in mathematics, statistics and the sciences; in concludes with topics usually found at graduate level. Highlights include new sections on sampling and Markov chain Monte Carlo, geometric probability, coupling and Poisson approximation, large deviations, spatial Poisson processes, renewal-reward, queueing networks, stochastic calculus, Itô's formula and option pricing in the Black-Scholes model for financial markets.
- Events and their probabilities
- Random variables and their distribution
- Discrete random variables
- Continuous random variables
- Generating functions and their applications
- Markov chains
- Convergence of random variables
- Random processes
- Stationary processes
- Diffusion processes