This book is based on a course given at Massachusetts Institute of
Technology. It is intended to be a reasonably self-contained
introduction to stochastic analytic techniques that can be used in
the study of certain problems. The central theme is the theory of
diffusions. In order to emphasize the intuitive aspects of
probabilistic techniques, diffusion theory is presented as a
natural generalization of the flow generated by a vector field.
Essential to the development of this idea is the introduction of
martingales and the formulation of diffusion theory in terms of
martingales. The book will make valuable reading for advanced
students in probability theory and analysis and will be welcomed as
a concise account of the subject by research workers in these
fields.
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