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...Stochastic calculus an introduction with applications gregory f lawler all rights reserved ii contents martingales in discrete time conditional expectation optional sampling theorem martingale convergence square integrable integrals respect to random walk amaximal inequality exercises brownian motion limits of sums independent variables multivariate normal distribution walks construction understanding as a continuous markov process gaussian self similar computations for quadratic variation multidimensional heat equation and generator one dimension expected value at future iii iv integration what is integral review riemann simple processes it o s formula more versions diusions covariation the product rule several motions local example bessel feynman kac binomial approximations change measure girsanov absolutely measures giving drift black scholes approach pricing representation jump l evy poisson compound generalized i...