Closure method and asymptotic expansions for linear stochastic systems
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In this article, a closure procedure for the hierarchy of moment equations related to linear systems of ordinary differential equations with a random parametric excitation is introduced, and a generalization of Pringsheim's theorem for continued fractions is used in a proof of the procedure convergence.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2007-05-01 and is currently open access. It has received 18 citations till now. The article focuses on the topics: Method of matched asymptotic expansions & Singular perturbation.read more
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Book ChapterDOI
Moment Closure—A Brief Review
TL;DR: A brief review of moment closure methods can be found in this article, where the authors focus on highlighting how moment closure can be used in different contexts and conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work well in practice.
Journal ArticleDOI
Transitions in a Duffing oscillator excited by random noise
R. V. Bobryk,A. Chrzeszczyk +1 more
TL;DR: In this article, the authors investigate a Duffing oscillator driven by random noise, which is assumed to be a harmonic function of the Wiener process, and show that the correlation time of the noise has a strong effect on the form of the response stationary probability density functions.
Journal ArticleDOI
Stability regions for Mathieu equation with imperfect periodicity
R.V. Bobryk,A. Chrzeszczyk +1 more
TL;DR: In this article, a mean square stability for the Mathieu equation with a random phase modulation in parametric excitation is considered and an efficient numerical scheme is proposed for obtaining the stability charts for this equation.
Journal ArticleDOI
Stochastic multiresonance in oscillators induced by bounded noise
TL;DR: Stochastic resonance (SR) in a harmonic oscillator with parametric bounded noise and external periodic force is investigated and it is shown that similar effects can be observed in the case of harmonic noise external force.
References
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Book
Stochastic processes in physics and chemistry
TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.
Stochastic Processes in Physics and Chemistry
Abstract: Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master equation. VI. One-step processes. VII. Chemical reactions. VIII. The Fokker-Planck equation. IX. The Langevin approach. X. The expansion of the master equation. XI. The diffusion type. XII. First-passage problems. XIII. Unstable systems. XIV. Fluctuations in continuous systems. XV. The statistics of jump events. XVI. Stochastic differential equations. XVII. Stochastic behavior of quantum systems.
Book
Continued Fractions: Analytic Theory and Applications
William B. Jones,W. J. Thron +1 more
TL;DR: In this paper, the authors present a method for representing analytic functions by continued fractions and apply it to the birth-death process (BDP) in the context of continuous fractions.
Book
Probabilistic Structural Dynamics: Advanced Theory and Applications
TL;DR: Spectral analysis evolutionary spectral analysis Markov processes exact solutions for multi-dimensional nonlinear systems stability of stochastic systems approximate solutions for first-excursion failure disordered structures as discussed by the authors.