Generalized Diffusion Processes (Translations of Mathematical Monographs, Book 83)
Generalized Diffusion Processes (Translations of Mathematical Monographs, Book 83) by N. I. Portenko
English | 1990 | ISBN: 0821845381 | ISBN-13: 9780821845387 | 180 pages | PDF | 2,9 MB
English | 1990 | ISBN: 0821845381 | ISBN-13: 9780821845387 | 180 pages | PDF | 2,9 MB
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.