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Stochastic Calculus: An Introduction with Applications

Stochastic calculus : An Introduction withApplicationsGregory F. Lawler 2014 Gregory F. LawlerAll rights reservediiContents1 Martingales in discrete Conditional expectation .. Martingales .. Optional sampling theorem .. Martingale convergence theorem .. Square integrable martingales .. Integrals with respect to random walk .. A maximal inequality .. Exercises .. 282 Brownian Limits of sums of independent variables .. Multivariate normal distribution .. Limits of random walks .. Brownian motion .. Construction of Brownian motion .. Understanding Brownian motion .. motion as a continuous martingale .. motion as a Markov process .. motion as a Gaussian process .. motion as a self-similar process .. Computations for Brownian motion .. Quadratic variation.

This is an introduction to stochastic calculus. I will assume that the reader has had a post-calculus course in probability or statistics. For much of these notes this is all that is needed, but to have a deep understanding of the subject, one needs to know measure theory and probability from that per-spective.

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