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Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order,ε-dependent parabolic partial differential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the...
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 onView the MathML sourcewhich are slightly stronger than those required to prove...