The Itô integral carries the notion of a martingale transform from discrete time into continuous time. The construction gives us a systematic method for building new martingales, and it leads to a new calculus for stochastic processes, the consequences of which turn out to be more far reaching than anyone could have possibly expected. The Itô calculus is now well established as one of the most useful tools of probability theory.
KeywordsTriangle Inequality Cauchy Sequence Dense Subset Integral Sign Approximation Theorem
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