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Fractional Stability of Diffusion Approximation for Random Differential Equations

Yuriy V. Kolomiets

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We consider the systems of random differential equations. The coefficients of the equations depend on a small parameter. The first equation, “slow” component, Ordinary Differential Equation (ODE), has unbounded highly oscillating in space variable coefficients and random perturbations, which are described by the second equation, “fast” component, Stochastic Differential Equation (SDE) with periodic coefficients. Sufficient conditions for weak convergence as small parameter goes to zero of the solutions of the “slow” components to the certain stochastic process are given.

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Stewart N. Ethier, Jin Feng and Richard H. Stockbridge, eds., Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 41-61

First available in Project Euclid: 28 January 2009

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Kolomiets, Yuriy V. Fractional Stability of Diffusion Approximation for Random Differential Equations. Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz, 41--61, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000291.

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