Dynamical systems driven by small white noise: Asymptotic analysis and applications

1983 ◽  
pp. 2-34
Author(s):  
Z. Schuss ◽  
B. J. Matkowsky
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Analysis ◽  
White Noise

Composition and invariance methods for solving some stochastic control problems

1975 ◽  
Vol 7 (02) ◽  
pp. 299-329 ◽  
Author(s):  
V. E. Beneš
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamical Systems ◽  
White Noise ◽  
Stochastic Control ◽  
Analytical Methods ◽  
Control Problems ◽  
Numerical Treatment ◽  
Partial Differential ◽  
Stochastic Control Problems

This paper considers certain stochastic control problems in which control affects the criterion through the process trajectory. Special analytical methods are developed to solve such problems for certain dynamical systems forced by white noise. It is found that some control problems hitherto approachable only through laborious numerical treatment of the non-linear Bellman-Hamilton-Jacobi partial differential equation can now be solved.

scholarly journals APPROXIMATION OF INVARIANT FOLIATIONS FOR STOCHASTIC DYNAMICAL SYSTEMS

2012 ◽  
Vol 12 (01) ◽  
pp. 1150011 ◽  
Author(s):  
XU SUN ◽  
XINGYE KAN ◽  
JINQIAO DUAN
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Analysis ◽  
Nonlinear Dynamical Systems ◽  
Random Sets ◽  
Stochastic Dynamical Systems ◽  
Geometric Structures ◽  
Nonlinear Dynamical

Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random sets. Thus it is desirable to have some techniques to approximate random invariant foliations. In this paper, invariant foliations are approximated for dynamical systems with small noisy perturbations, via asymptotic analysis. Namely, random invariant foliations are represented as a perturbation of the deterministic invariant foliations, with deviation errors estimated.

Asymptotic analysis of kinematically excited dynamical systems near resonances

2011 ◽  
Vol 68 (4) ◽  
pp. 459-469 ◽  
Author(s):  
Roman Starosta ◽  
Grażyna Sypniewska-Kamińska ◽  
Jan Awrejcewicz
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Analysis

scholarly journals Random Attractors for Stochastic Retarded Lattice Dynamical Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Xiaoquan Ding ◽  
Jifa Jiang
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
White Noise ◽  
Random Attractor ◽  
Additive White Noise ◽  
Lattice Dynamical System ◽  
Random Attractors ◽  
Lattice Dynamical Systems ◽  
Bounded Sets

This paper is devoted to a stochastic retarded lattice dynamical system with additive white noise. We extend the method of tail estimates to stochastic retarded lattice dynamical systems and prove the existence of a compact global random attractor within the set of tempered random bounded sets.

scholarly journals Impact of Correlated Noises on Additive Dynamical Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Chujin Li ◽  
Jinqiao Duan
Keyword(s):  
Dynamical Systems ◽  
White Noise ◽  
Probability Density ◽  
Probability Density Functions ◽  
Hurst Parameter ◽  
Random Solution ◽  
Small Noise ◽  
Fractional Brownian Motions ◽  
Noise Limit ◽  
Correlated Noises

Impact of correlated noises on dynamical systems is investigated by considering Fokker-Planck type equations under the fractional white noise measure, which correspond to stochastic differential equations driven by fractional Brownian motions with the Hurst parameterH>1/2. Firstly, by constructing the fractional white noise framework, one small noise limit theorem is proved, which provides an estimate for the deviation of random solution orbits from the corresponding deterministic orbits. Secondly, numerical experiments are conducted to examine the probability density evolutions of two special dynamical systems, as the Hurst parameterHvaries. Certain behaviors of the probability density functions are observed.

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