Singular perturbations for a subelliptic operator
2018 ◽
Vol 24
(4)
◽
pp. 1429-1451
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Keyword(s):
We study some classes of singular perturbation problems where the dynamics of the fast variables evolve in the whole space obeying to an infinitesimal operator which is subelliptic and ergodic. We prove that the corresponding ergodic problem admits a solution which is globally Lipschitz continuous and it has at most a logarithmic growth at infinity. The main result of this paper establishes that, as ϵ → 0, the value functions of the singular perturbation problems converge locally uniformly to the solution of an effective problem whose operator and terminal data are explicitly given in terms of the invariant measure for the ergodic operator.
1966 ◽
Vol 23
(1)
◽
pp. 26-86
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1992 ◽
Vol 9
(2)
◽
pp. 143-155
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1998 ◽
Vol 92
(2-3)
◽
pp. 101-123
◽
1997 ◽
Vol 77
(1)
◽
pp. 59-74
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2013 ◽
Vol 5
(4)
◽
pp. 250-257
2016 ◽
Vol 9
(1)
◽
pp. 53
◽
Variable mesh non polynomial spline method for singular perturbation problems exhibiting twin layers
2019 ◽
Vol 1344
◽
pp. 012011