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• W2000436082 abstract "Consider diffusions on $mathbb{R}^k > 1$, governed by the Itô equation $dX(t) = {b(X(t)) + beta(X(t)/a)} dt + sigmadB(t)$, where $b, beta$ are periodic with the same period and are divergence free, $sigma$ is nonsingular and a is a large integer. Two distinct Gaussian phases occur as time progresses. The initial phase is exhibited over times $1 ll t ll a^{2/3}$. Under a geometric condition on the velocity field $beta$, the final Gaussian phase occurs for times $t gg a^2(log a)^2$, and the dispersion grows quadratically with a . Under a complementary condition, the final phase shows up at times $t gg a^4(log a)^2$, or $t gg a^2 log a$ under additional conditions, with no unbounded growth in dispersion as a function of scale. Examples show the existence of non-Gaussian intermediate phases. These probabilisitic results are applied to analyze a multiscale Fokker-Planck equation governing solute transport in periodic porous media. In case $b, beta$ are not divergence free, some insight is provided by the analysis of one-dimensional multiscale diffusions with periodic coefficients." @default.
• W2000436082 created "2016-06-24" @default.
• W2000436082 creator A5010740475 @default.
• W2000436082 date "1999-11-01" @default.
• W2000436082 modified "2023-10-03" @default.
• W2000436082 title "Multiscale diffusion processes with periodic coefficients and an application to solute transport in porous media" @default.
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• W2000436082 doi "https://doi.org/10.1214/aoap/1029962863" @default.
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