Regularly varying correlation functions and KMO-Langevin equations
Akihiko Inoue · Hokkaido Mathematical Journal · 1997
We study a variant of Okabe's first KMO-Langevin equation.After establishing unique existence of a stationary solution, we precisely describe the long-time behavior of the correlation function R of the solution.In particular, the behavior such as R(t)\sim ct^{-1} as tarrow\infty is characterized by using \Pi -variation.Correlation functions regularly varying with index p\in [-1,0) are characterized in terms of outer functions.