Direct modeling of white noise in stochastic systems

2005 ◽  
pp. 1-30 ◽  
Author(s):  
Arunabha Bagchi ◽  
Ravi Mazumdar
Keyword(s):  
White Noise ◽  
Stochastic Systems ◽  
Direct Modeling

scholarly journals Weighted Measurement Fusion White Noise Deconvolution Filter with Correlated Noise for Multisensor Stochastic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Xin Wang ◽  
Shu-Li Sun ◽  
Kai-Hui Ding ◽  
Jing-Yan Xue
Keyword(s):  
White Noise ◽  
Stochastic Systems ◽  
Gaussian White Noise ◽  
Minimum Variance ◽  
Seismic Exploration ◽  
Global Optimality ◽  
Correlated Noise ◽  
Noise Input ◽  
Time Invariant ◽  
Correlated Noises

For the multisensor linear discrete time-invariant stochastic control systems with different measurement matrices and correlated noises, the centralized measurement fusion white noise estimators are presented by the linear minimum variance criterion under the condition that noise input matrix is full column rank. They have the expensive computing burden due to the high-dimension extended measurement matrix. To reduce the computing burden, the weighted measurement fusion white noise estimators are presented. It is proved that weighted measurement fusion white noise estimators have the same accuracy as the centralized measurement fusion white noise estimators, so it has global optimality. It can be applied to signal processing in oil seismic exploration. A simulation example for Bernoulli-Gaussian white noise deconvolution filter verifies the effectiveness.

Random attractors of FitzHugh–Nagumo systems driven by colored noise on unbounded domains

2019 ◽  
Vol 19 (05) ◽  
pp. 1950035
Author(s):  
Anhui Gu ◽  
Bixiang Wang
Keyword(s):  
Asymptotic Behavior ◽  
White Noise ◽  
Correlation Time ◽  
Existence And Uniqueness ◽  
Colored Noise ◽  
Stochastic Systems ◽  
Unbounded Domains ◽  
Limiting Behavior ◽  
Uniform Estimates ◽  
Random Attractors

We investigate the pathwise asymptotic behavior of the FitzHugh–Nagumo systems defined on unbounded domains driven by nonlinear colored noise. We prove the existence and uniqueness of tempered pullback random attractors of the systems with polynomial diffusion terms. The pullback asymptotic compactness of solutions is obtained by the uniform estimates on the tails of solutions outside a bounded domain. We also examine the limiting behavior of the FitzHugh–Nagumo systems driven by linear colored noise as the correlation time of the colored noise approaches zero. In this respect, we prove that the solutions and the pullback random attractors of the systems driven by linear colored noise converge to that of the corresponding stochastic systems driven by linear white noise.

Statistics of an Appealing Class of Random Processes

2021 ◽  
pp. 260-276
Author(s):  
Shaival Hemant Nagarsheth ◽  
Shambhu Nath Sharma
Keyword(s):  
White Noise ◽  
Stochastic Systems ◽  
Correction Term ◽  
Random Processes ◽  
Random Perturbations ◽  
White Noise Process ◽  
Coloured Noise ◽  
Diffusion Operator ◽  
Noise Process ◽  
Special Cases

The white noise process, the Ornstein-Uhlenbeck process, and coloured noise process are salient noise processes to model the effect of random perturbations. In this chapter, the statistical properties, the master's equations for the Brownian noise process, coloured noise process, and the OU process are summarized. The results associated with the white noise process would be derived as the special cases of the Brownian and the OU noise processes. This chapter also formalizes stochastic differential rules for the Brownian motion and the OU process-driven vector stochastic differential systems in detail. Moreover, the master equations, especially for the coloured noise-driven stochastic differential system as well as the OU noise process-driven, are recast in the operator form involving the drift and modified diffusion operators involving an additional correction term to the standard diffusion operator. The results summarized in this chapter will be useful for modelling a random walk in stochastic systems.

scholarly journals Derivation of Fokker–Planck equations for stochastic systems under excitation of multiplicative non-Gaussian white noise

2017 ◽  
Vol 446 (1) ◽  
pp. 786-800 ◽  
Author(s):  
Xu Sun ◽  
Jinqiao Duan ◽  
Xiaofan Li ◽  
Hua Liu ◽  
Xiangjun Wang ◽  
...  
Keyword(s):  
White Noise ◽  
Stochastic Systems ◽  
Gaussian White Noise ◽  
Non Gaussian ◽  
Fokker Planck Equations ◽  
Fokker Planck
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