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Invariance Principles for Parabolic Equations with Random Coefficients

✍ Scribed by Donald A. Dawson; Michael A. Kouritzin

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 535 KB
Volume: 149
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3107

No coin nor oath required. For personal study only.

✦ Synopsis

A general Hilbert-space-based stochastic averaging theory is brought forth herein for arbitrary-order parabolic equations with (possibly long range dependent) random coefficients. We use regularity conditions on t u = (t, x)= :

which are slightly stronger than those required to prove pathwise existence and uniqueness for (1). Equation (1) can be obtained from the singularly perturbed system

through time change. Next, we impose on the coefficients of (1) a pointwise (in x and t) weak law of large numbers and a weak invariance principle

, H 1 being a separable Hilbert space of functions and h # (0, 1) denoting a constant. (h>1Â2 allows for long range time dependence.

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