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Diffusion Processes, Jump Processes, and Stochastic Differential Equations provides a compact exposition of the results explaining interrelations between di?usion stochastic processes, stochastic di?erential equations and the fractional in?nitesimal operators. The draft of this book has been extensively classroom tested by the author at Case Western Reserve University in a course that enrolled seniors and graduate students majoring in mathematics, statistics, engineering, physics, chemistry, economics and mathematical ?nance. The last topic proved to be particularly popular among students looking for careers on Wall Street and in research organizations devoted to ?nancial problems. Features Quickly and concisely builds from basic probability theory to advanced topics Suitable as a primary text for an advanced course in diffusion processes and stochastic differential equations Useful as supplementary reading across a range of topics.