Stochastic averaging with a flattened hamiltonian: A Markov process on a stratified space (a whiskered sphere)

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)853-900
Number of pages48
JournalTransactions of the American Mathematical Society
Volume354
Issue number3
DOIs
StatePublished - 2002

Keywords

  • Markov processes
  • Stochastic averaging
  • Stratified space

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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