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Fractional Stability of Diffusion Approximation for Random Differential Equations

Yuriy V. Kolomiets

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Abstract

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.

Chapter information

Source
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

Dates
First available in Project Euclid: 28 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1233152934

Digital Object Identifier
doi:10.1214/074921708000000291

Mathematical Reviews number (MathSciNet)
MR2574223

Zentralblatt MATH identifier
1171.60351

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

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. https://projecteuclid.org/euclid.imsc/1233152934


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