TY - JOUR

T1 - Stochastic averaging with a flattened hamiltonian

T2 - A Markov process on a stratified space (a whiskered sphere)

AU - Sowers, Richard B.

PY - 2002

Y1 - 2002

N2 - We consider a random perturbation of a 2-dimensional Hamiltonian ODE. Under an appropriate change of time, we identify a reduced model, which in some aspects is similar to a stochastically averaged model. The novelty of our problem is that the set of critical points of the Hamiltonian has an interior. Thus we can stochastically average outside this set of critical points, but inside we can make no model reduction. The result is a Markov process on a stratified space which looks like a whiskered sphere (i.e, a 2-dimensional sphere with a line attached). At the junction of the sphere and the line, glueing conditions identify the behavior of the Markov process.

AB - We consider a random perturbation of a 2-dimensional Hamiltonian ODE. Under an appropriate change of time, we identify a reduced model, which in some aspects is similar to a stochastically averaged model. The novelty of our problem is that the set of critical points of the Hamiltonian has an interior. Thus we can stochastically average outside this set of critical points, but inside we can make no model reduction. The result is a Markov process on a stratified space which looks like a whiskered sphere (i.e, a 2-dimensional sphere with a line attached). At the junction of the sphere and the line, glueing conditions identify the behavior of the Markov process.

KW - Markov processes

KW - Stochastic averaging

KW - Stratified space

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U2 - 10.1090/S0002-9947-01-02903-8

DO - 10.1090/S0002-9947-01-02903-8

M3 - Article

AN - SCOPUS:0035993959

VL - 354

SP - 853

EP - 900

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -