TY - JOUR
T1 - Averaging of stochastic flows
T2 - Twist maps and escape from resonance
AU - Sowers, Richard B.
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under Grant Nos. 0305925 and 0604249.
PY - 2009/10
Y1 - 2009/10
N2 - Our setup is a classical stochastic averaging one studied by Has'minskiǐ, which is a two-dimensional SDE (on a cylinder) consisting of a fast angular drift and a slow axial diffusion. We seek to understand the asymptotics of the flow generated by this SDE. To do so, we fix n initial points on the cylinder and consider the axial components of the trajectories evolving from these points. We conclude a propagation-of-chaos. There are two components of the limiting n-point motion: a common Brownian motion, and n independent Brownian motions, one for each initial point.
AB - Our setup is a classical stochastic averaging one studied by Has'minskiǐ, which is a two-dimensional SDE (on a cylinder) consisting of a fast angular drift and a slow axial diffusion. We seek to understand the asymptotics of the flow generated by this SDE. To do so, we fix n initial points on the cylinder and consider the axial components of the trajectories evolving from these points. We conclude a propagation-of-chaos. There are two components of the limiting n-point motion: a common Brownian motion, and n independent Brownian motions, one for each initial point.
KW - Escape from resonance
KW - Stochastic averaging
KW - Stochastic flows of diffeomorphisms
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U2 - 10.1016/j.spa.2009.04.004
DO - 10.1016/j.spa.2009.04.004
M3 - Article
AN - SCOPUS:69749086132
VL - 119
SP - 3549
EP - 3582
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 10
ER -