Abstract
We present a history of the development of the theory of Stochastic Integration, starting from its roots with Brownian motion, up to the introduction of semimartingales and the independence of the theory from an underlying Markov process framework. We show how the development has influenced and in turn been influenced by the development of Mathematical Finance Theory. The calendar period is from 1880 to 1970.
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Digital Object Identifier: 10.1214/lnms/1196285381