STABILITY OF ORDINARY DIFFERENTIAL EQUATIONS WITH COLORED NOISE FORCING

被引：3

作者：

Blass, Timothy ^{[1
]}

Romero, L. A. ^{[2
]}

机构：

[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

[2] Sandia Natl Labs, Computat Math & Algorithms Dept, Albuquerque, NM 87123 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 02期

基金：

美国国家科学基金会;

关键词：

colored noise; parametric forcing; moment stability; Fokker-Planck operator; ladder operators; FOKKER-PLANCK; OPERATORS;

D O I：

10.1137/110855302

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present a perturbation method for determining the moment stability of linear ordinary differential equations with parametric forcing by colored noise. In particular, the forcing arises from passing white noise through an nth order filter. We carry out a perturbation analysis based on a small parameter e that gives the amplitude of the forcing. Our perturbation analysis is based on a ladder operator approach to the vector Ornstein-Uhlenbeck process. We can carry out our perturbation expansion to any order in e, for a large class linear filters, and for quite arbitrary linear systems. As an example we apply our results to the stochastically forced Mathieu equation.

引用

页码：1099 / 1127

页数：29

共 25 条

[11]

Blass T., 2012, SAND20126980 SAND NA

[12] Colored-noise-induced parametric resonance [J].

Bobryk, RV ;

Chrzeszczyk, A .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2002, 316 (1-4) :225-232

[13] ON THE CONTROLLABILITY OF MATRIX PAIRS (A,K) WITH K POSITIVE SEMIDEFINITE [J].

CARLSON, D ;

DATTA, BN ;

SCHNEIDER, H .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1984, 5 (03) :346-350

[14]

Dirac P. A. M., 1930, PRINCIPLES QUANTUM M

[15]

GARDINER CW, 1985, SPRINGER SER SYNERGE, V13

[16]

Khasminski R. Z., 1980, STOCHASTIC STABILITY

[17] A general scheme for studying the stochastic dynamics of a parametric oscillator driven by coloured noise [J].

Lee, HJ ;

Kim, C ;

Kim, JG ;

Lee, EK .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (03) :647-656

[18] Spectral analysis of Fokker-Planck and related operators arising from linear stochastic differential equations [J].

Liberzon, D ;

Brockett, RW .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (05) :1453-1467

[19] Spectrum of Ornstein-Uhlenbeck operators in Lp spaces with respect to invariant measures [J].

Metafune, G ;

Pallara, D ;

Priola, E .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 196 (01) :40-60

[20] Finite amplitude Faraday waves induced by a random forcing [J].

Repetto, R ;

Galletta, V .

PHYSICS OF FLUIDS, 2002, 14 (12) :4284-4289

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