On the asymptotic equivalence and rate of convergence of nonparametric regression and Gaussian white noise

2004 ◽  
Vol 22 (3-2004) ◽  
pp. 235-243 ◽  
Author(s):  
Angelika Rohde
Keyword(s):  
White Noise ◽  
Rate Of Convergence ◽  
Nonparametric Regression ◽  
Gaussian White Noise ◽  
Asymptotic Equivalence

scholarly journals Asymptotic equivalence of nonparametric regression and white noise

1996 ◽  
Vol 24 (6) ◽  
pp. 2384-2398 ◽  
Author(s):  
Lawrence D. Brown ◽  
Mark G. Low
Keyword(s):  
White Noise ◽  
Nonparametric Regression ◽  
Asymptotic Equivalence

scholarly journals Local asymptotic equivalence of pure states ensembles and quantum Gaussian white noise

2018 ◽  
Vol 46 (6B) ◽  
pp. 3676-3706
Author(s):  
Cristina Butucea ◽  
Mădălin Guţă ◽  
Michael Nussbaum
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Asymptotic Equivalence ◽  
Pure States

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

Sign in / Sign up

Export Citation Format

Share Document