Asymptotic analysis of nonlinear stochastic equations with rapidly oscillating and decaying components

N. Sri Namachchivaya, H. J. Van Roessel

Research output: Contribution to journalConference article

Abstract

We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.

Original languageEnglish (US)
Pages (from-to)277-286
Number of pages10
JournalAmerican Society of Mechanical Engineers, Applied Mechanics Division, AMD
Volume254
DOIs
StatePublished - Jan 1 2003
Event2003 ASME International Mechanical Engineering Congress - Washington, DC., United States
Duration: Nov 15 2003Nov 21 2003

Fingerprint

Nonlinear dynamical systems
Asymptotic analysis
Markov processes

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Asymptotic analysis of nonlinear stochastic equations with rapidly oscillating and decaying components. / Sri Namachchivaya, N.; Van Roessel, H. J.

In: American Society of Mechanical Engineers, Applied Mechanics Division, AMD, Vol. 254, 01.01.2003, p. 277-286.

Research output: Contribution to journalConference article

@article{729c9f4173e746d9a4f0b19cb3c0e36e,
title = "Asymptotic analysis of nonlinear stochastic equations with rapidly oscillating and decaying components",
abstract = "We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.",
author = "{Sri Namachchivaya}, N. and {Van Roessel}, {H. J.}",
year = "2003",
month = "1",
day = "1",
doi = "10.1115/IMECE2003-55648",
language = "English (US)",
volume = "254",
pages = "277--286",
journal = "American Society of Mechanical Engineers, Applied Mechanics Division, AMD",
issn = "0160-8835",

}

TY - JOUR

T1 - Asymptotic analysis of nonlinear stochastic equations with rapidly oscillating and decaying components

AU - Sri Namachchivaya, N.

AU - Van Roessel, H. J.

PY - 2003/1/1

Y1 - 2003/1/1

N2 - We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.

AB - We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.

UR - http://www.scopus.com/inward/record.url?scp=1842426590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842426590&partnerID=8YFLogxK

U2 - 10.1115/IMECE2003-55648

DO - 10.1115/IMECE2003-55648

M3 - Conference article

AN - SCOPUS:1842426590

VL - 254

SP - 277

EP - 286

JO - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

JF - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

SN - 0160-8835

ER -