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Multidimensional Diffusion Processes is written by Daniel W. Stroock and published by Springer Science & Business Media. It's available with International Standard Book Number or ISBN identification 3540903534 (ISBN 10) and 9783540903536 (ISBN 13).
From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik