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

N. Sri Namachchivaya; H. J. Van Roessel

doi:10.1115/IMECE2003-55648

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

N. Sri Namachchivaya
, H. J. Van Roessel

Aerospace Engineering

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

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 language	English (US)
Pages (from-to)	277-286
Number of pages	10
Journal	American Society of Mechanical Engineers, Applied Mechanics Division, AMD
Volume	254
DOIs	https://doi.org/10.1115/IMECE2003-55648
State	Published - 2003
Event	2003 ASME International Mechanical Engineering Congress - Washington, DC., United States Duration: Nov 15 2003 → Nov 21 2003

ASJC Scopus subject areas

Mechanical Engineering

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10.1115/IMECE2003-55648

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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.",

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year = "2003",

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note = "2003 ASME International Mechanical Engineering Congress ; Conference date: 15-11-2003 Through 21-11-2003",

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AU - Sri Namachchivaya, N.

AU - Van Roessel, H. J.

PY - 2003

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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.

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UR - https://www.scopus.com/pages/publications/1842426590#tab=citedBy

U2 - 10.1115/IMECE2003-55648

DO - 10.1115/IMECE2003-55648

M3 - Conference article

AN - SCOPUS:1842426590

SN - 0160-8835

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

T2 - 2003 ASME International Mechanical Engineering Congress

Y2 - 15 November 2003 through 21 November 2003

ER -

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

Abstract

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