This book provides a compact exposition of the results explaining interrelations between diﬀusion stochastic processes, SDEs and the fractional inﬁnitesimal operators. The draft of this book has been extensively classroom tested by the author at CWRU in a course that enrolled seniors and graduate students.

�ber die Autorin bzw. den Autor:

Wojbor A. Woyczyński was a mathematics and statistics professor, who was born and educated in Poland. He earned his M.Sc. in Electrical and Computer Engineering at Wroclaw University of Technology in 1966, and his Ph.D. in Mathematics, at the University of Wroclaw in 1968, when he was 23 years old. He spent most of his career teaching at Case Western Reserve University in Cleveland, Ohio, USA where he started working in 1982, when he was hired as chair of the Department of Mathematics and Statistics. He published over 160 papers and many books, including this, his 18th book, delving into a wide array of topics in mathematics. His research interests stretched from mainstream probability theory, to mathematical physics and turbulence theory, operations research and financial mathematics, to mathematical biology. In 1992 he published a monograph on “Random Series and Stochastic Integrals”, co-written with Stanis law Kwapień. The paper “L�vy Flights in Evolutionary Ecology,” co-written with two French mathematicians, Sylvie M�l�ard and Benjamin Jourdain, won the 2013 prize La Recherche for the best work in the field of mathematics. He published a number of works honoring the great mathematicians of preceding generations. Early in his career, in 1986, he was elected as a Fellow of the Institute of Mathematics. He served as an editorial board member of Probability and Mathematical Statistics, Annals of Applied Probability, and Stochastic Processes and Their Applications. This book was published posthumously, with the consent of his family.

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Diffusion Processes, Jump Processes, and Stochastic Differential Equations

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