TY - JOUR
T1 - Rigorous stochastic averaging at a center with additive noise
AU - Namachchivaya, N. Sri
AU - Sowers, Richard B.
N1 - Funding Information:
The authors would like to acknowledge the support of the Office of Naval Research under grant number N001-15-005, and National Science Foundation under grant numbers CMS 00-84944 and DMS 00-71484.
PY - 2002
Y1 - 2002
N2 - We consider a random perturbation of a two-dimensional Hamiltonian system with an isolated elliptic fixed point; that is, a center. Under an appropriate change of time, we identify a reduced stochastically-averaged model. We give a rigorous proof of averaging at the center. Our main technique is to use the martingale problem. Our formulation of the result is in a sufficiently abstract setting that it agrees with more complicated averaging results.
AB - We consider a random perturbation of a two-dimensional Hamiltonian system with an isolated elliptic fixed point; that is, a center. Under an appropriate change of time, we identify a reduced stochastically-averaged model. We give a rigorous proof of averaging at the center. Our main technique is to use the martingale problem. Our formulation of the result is in a sufficiently abstract setting that it agrees with more complicated averaging results.
KW - Hamiltonian
KW - Markov processes
KW - Martingale problem
KW - Stochastic averaging
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U2 - 10.1023/A:1019614613583
DO - 10.1023/A:1019614613583
M3 - Conference article
AN - SCOPUS:0036374167
VL - 37
SP - 85
EP - 114
JO - Meccanica
JF - Meccanica
SN - 0025-6455
IS - 1-2
T2 - Euromech Colloquium No. 413
Y2 - 12 June 2000 through 14 June 2000
ER -