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Markov Processes from K. Ito's Perspective (AM-155) by Daniel W. Stroock (Paperback, 2003)

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Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. The modern theory of Markov processes was initiated by A. N. Kolmogorov.