Stochastic Averaging for a Hamiltonian System with Skew Random Perturbations

Chetan D. Pahlajani ()
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Chetan D. Pahlajani: University of Delaware

Journal of Theoretical Probability, 2015, vol. 28, issue 3, 1165-1226

Abstract: Abstract We consider a stochastic process that arises due to small random perturbations of a particle moving along the orbits of a double-well Hamiltonian. The perturbing noise is assumed to have skewness along the infinity-shaped homoclinic orbit of the Hamiltonian. As the noise strength goes to zero, we characterize the limiting dynamics in terms of a graph-valued Markov process. The effort centers around the construction of certain perturbed test functions needed to prove convergence. Following Sowers, we accomplish this through the development of suitable corrector functions in a boundary layer near the homoclinic orbit.

Keywords: Stochastic averaging; Skew diffusion; Hamiltonian; 60F17 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10959-013-0533-9

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