Generalized Diffusion Processes

Nikola_ Ivanovich Portenko

1990년 12월 · Translations of Mathematical Monographs 83권 · American Mathematical Soc.

eBook

180

페이지

검증되지 않은 평점과 리뷰입니다. 자세히 알아보기

eBook 정보

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.