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Many practitioners are familiar with elementary probability theory, but need to learn stochastic calculus. Between these two topics, there is a vast gulf of knowledge that needs to be filled in. The linchpin is a measure-theoretic treatment of probability theory. Many texts offer this in a manner that caters to mathematicians. I like Resnick because it is rigorous but caters primarily to non-mathematicians. The book is goal-oriented and avoids needless formality. Resnick introduces measure theory as you progress through the book, so the material is accessible to anyone who has read Apostle (1974) or a similar text in advanced calculus. However, learning may be easier if you have already read a basic measure theory book such as Bartle (1966). |
Building from basic principals, Resnick covers random variables, independence, expectations, convergence theorems, the law of large numbers, the central limit theorem and martingales. The book closes with a discussion of how martingales are used in finance. Almost twice as long as the competing Williams (1991), Resnick covers less material. I recommend Resnick because it is well written and offers practitioners the most accessible introduction to measure-theoretic probability that I am aware of. It is a rigorous but accessible route to the foundations of stochastic calculus.
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