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Generalized Diffusion Processes
N. I. Portenko
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Translations of Mathematical Monographs
1990; 180 pp; hardcover
Volume: 83
ISBN-10: 0-8218-4538-1
ISBN-13: 978-0-8218-4538-7
List Price: US$88
Member Price: US$70.40
Order Code: MMONO/83
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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
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