Looking for good books about simulating stochastic processes.

Question

Yes, like the title says im looking for books about simulating stochastic processes.

If they are using R in the book its great.

If they are using matlab its good too or if they are just describing the simulations without any specific programming language in mind its also ok but i prefer to see some code.

Here are some examples of simulation problems im interested in.

• Queues (M/M/1, M/M/S, M/M/S/K etc)
• Continous and discrete Markov chains
• Birth and death processess
• Wiener processes
• Martingales and stopping times
• Things like estimating P(X(t)=k), t in some interval, for some process or approximating the density function for some process. etc

edit: We are not using stochastic differential equations at all in this course. The simulations is just a small part of the course and there is nothing about simulations in the course literature. But i find the simulations most fun and want to learn more about it. I have googled and checked the university library but found nothing useful.

Answer 1

I hesitate to answer broad and opinion-based questions because it is difficult the judge the expertise of those who answer. But this has been sitting here for a couple of weeks with no answers or comments. So here are some necessarily-biased comments that may be useful.

Roe Goodman Introduction to Stochastic Models (1988) simulates many stochastic processes, including some of the queues you mentioned. Continuous time is typically discretized to get Markov chains with transition matrices. Several of my colleagues have used this book for a text in an undergrad Stochastic processes course and have liked it.

You might find something useful in the literature on Markov Chain Monte Carlo, which deals almost entirely with simulation. A very elementary reference here is Suess Introduction to probability simulation and Gibbs Sampling with R (2010). But you may want to look more broadly using 'MCMC' to search.

Because Wiener processes are continuous in both states and time, compromises must be made for manageable simulations. (True sample paths are almost surely nowhere differentiable, and thus difficult to simulate realistically.)

Finally, you could pose specifics of one of your questions on this site and see what guidance flows from that. I have answered a couple of elementary questions on simulating Markov chains in the last few days, but they may be too elementary for you: take a look (last and recent).