Translations of Mathematical Monographs 1990; 180 pp; hardcover Volume: 83 ISBN10: 0821845381 ISBN13: 9780821845387 List Price: US$93 Member Price: US$74.40 Order Code: MMONO/83
 Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for diffusion in a medium moving in a nonregular way. The author constructs generalized diffusion processes under two assumptions: first, that the diffusion matrix is sufficiently regular; and second, that the drift vector is a function integrable to some power, or is a generalized function of the type of the derivative of a measure. Table of Contents  The method of absolutely continuous change of measure
 The analytic method
 Generalized diffusion processes
