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stochastic averaging method

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Second-order differential equations with random perturbations and small parameters
Part of
M. Kamenskii, S. Pergamenchtchikov, M. Quincampoix
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 4 / August 2017

Published online by Cambridge University Press:

05 July 2017, pp. 763-779

Print publication:

August 2017
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We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero.