When we compute the familiar integrals of Newton and Leibniz, we almost invariably call on the fundamental theorem of calculus — only a few integrals can be done comfortably by direct appeal to the definition. The situation with the Itô integral is parallel, and the Itô calculus would be stopped dead in its tracks if we could not find an appropriate analog to the traditional fundamental theorem of calculus. One of the great charms of Itô integration is that the required analog comes with an unexpected twist — and several probabilistic interpretations.
KeywordsBrownian Motion Harmonic Function Standard Process Quadratic Variation Standard Brownian Motion
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