Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 3, 741--762

PHASE CHANGES WITH TIME FOR A CLASS OF UTONOMOUS MULTISCALE DIFFUSIONS

By

RABI BHATTACHARYA, Indiana University, Bloomington, USA

SUMMARY. We obtain precise time scales for different Gaussian phases of a class of multiscale diffusions with periodic coefficients, improving earlier results. The first Gaussian phase occurs for times $1 \ll t \ll a^{2/3}$ where `$a$' is the large scale parameter, while the final Gaussian phase occurs for times $t \gg a^2$. Examples show that non-Gaussian phases appear between these two time zones. An application to a problem of solute transport in porous media is given, along with a survey of related literature.

*AMS (1991) subject classification}. *Primary 60J05; secondary 60H10, 60J70.

*Key words and phrases. *Diffusion on a torus, speed of convergence to equilibrium, Gaussian and non-Gaussian phases, growth in dispersivity.