Rigorous stochastic averaging at a center with additive noise

N. Sri Namachchivaya; Richard B. Sowers

doi:10.1023/A:1019614613583

Rigorous stochastic averaging at a center with additive noise

Research output: Contribution to journal › Conference article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	85-114
Number of pages	30
Journal	Meccanica
Volume	37
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1019614613583
State	Published - 2002
Event	Euromech Colloquium No. 413 - Palermo, Italy Duration: Jun 12 2000 → Jun 14 2000

Keywords

Hamiltonian
Markov processes
Martingale problem
Stochastic averaging

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

Online availability

10.1023/A:1019614613583

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title = "Rigorous stochastic averaging at a center with additive noise",

abstract = "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.",

keywords = "Hamiltonian, Markov processes, Martingale problem, Stochastic averaging",

author = "Namachchivaya, {N. Sri} and Sowers, {Richard B.}",

note = "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.; Euromech Colloquium No. 413 ; Conference date: 12-06-2000 Through 14-06-2000",

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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

SN - 0025-6455

VL - 37

SP - 85

EP - 114

JO - Meccanica

JF - Meccanica

IS - 1-2

T2 - Euromech Colloquium No. 413

Y2 - 12 June 2000 through 14 June 2000

ER -

Rigorous stochastic averaging at a center with additive noise

Abstract

Keywords

ASJC Scopus subject areas

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