Radically Elementary Probability Theory
Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
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Algebras of random variables
External analogues of internal notions
The decomposition of a stochastic process
Convergence of martingales
Fluctuations of martingales