scholarly journals On the derivation of the Nakajima-Zwanzig probability density function via white noise analysis

2017 ◽  
Author(s):  
Bienvenido M. Butanas ◽  
Roland C. F. Caballar
Keyword(s):  
Probability Density Function ◽  
White Noise ◽  
Probability Density ◽  
Density Function ◽  
Noise Analysis ◽  
White Noise Analysis

WHITE NOISE ANALYSIS: SOME APPLICATIONS IN COMPLEX SYSTEMS, BIOPHYSICS AND QUANTUM MECHANICS

2012 ◽  
Vol 26 (29) ◽  
pp. 1230014 ◽  
Author(s):  
CHRISTOPHER C. BERNIDO ◽  
M. VICTORIA CARPIO-BERNIDO
Keyword(s):  
Quantum Mechanics ◽  
Probability Density Function ◽  
Complex Systems ◽  
White Noise ◽  
Noise Analysis ◽  
Social Systems ◽  
White Noise Analysis ◽  
The Past ◽  
White Noise Calculus ◽  
With Memory

The white noise calculus originated by T. Hida is presented as a powerful tool in investigating physical and social systems. Combined with Feynman's sum-over-all histories approach, we parameterize paths with memory of the past, and evaluate the corresponding probability density function. We discuss applications of this approach to problems in complex systems and biophysics. Examples in quantum mechanics with boundaries are also given where Markovian paths are considered.

scholarly journals Analysis of exceedance probability of displacement response of randomly nonlinear structures

2000 ◽  
Vol 22 (4) ◽  
pp. 212-224 ◽  
Author(s):  
Luu Xuan Hung
Keyword(s):  
Probability Density Function ◽  
Nonlinear Systems ◽  
White Noise ◽  
Probability Density ◽  
Density Function ◽  
Exceedance Probability ◽  
Nonlinear Structures ◽  
Exact Probability ◽  
Displacement Response ◽  
Linearization Techniques

The paper presents the estimation of the exact exceedance probability (EEP) of stationary responses of some white noise-randomly excited nonlinear systems whose exact probability density function can be known. Consequently, the approximate exceedance probabilities (AEPs) are evaluated based on the analysis of equivalent linearized systems using the traditional Caughey method and the extension technique of LOMSEC. Comparisons of the AEPs versus the EEP are demonstrated. The obtained results indicate important characters of the exceedance probability (EP) as well as the influence of nonlinearity over EP. The evaluation of the applied possibility of the proposed linearization techniques for estimating AEPs are made.

Probability Density Function Solution of Nonlinear Oscillators Subjected to Multiplicative Poisson Pulse Excitation on Velocity

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
H. T. Zhu ◽  
G. K. Er ◽  
V. P. Iu ◽  
K. P. Kou
Keyword(s):  
Probability Density Function ◽  
White Noise ◽  
Probability Density ◽  
Density Function ◽  
Nonlinear Oscillators ◽  
Solution Procedure ◽  
Pulse Excitation ◽  
Poisson White Noise ◽  
White Noise Excitation ◽  
Fpk Equation

The stationary probability density function (PDF) solution of the stochastic responses is derived for nonlinear oscillators subjected to both additive and multiplicative Poisson white noises. The PDF solution is governed by the generalized Fokker–Planck–Kolmogorov (FPK) equation and obtained with the exponential-polynomial closure (EPC) method, which was originally proposed for solving the FPK equation. The extended EPC solution procedure is presented for the case of Poisson pulses in this paper. In order to evaluate the effectiveness of the solution procedure, nonlinear oscillators are investigated under multiplicative Poisson white noise excitation on velocity and additive Poisson white noise excitation. Both weakly and strongly nonlinear oscillators are considered, respectively. In the numerical analysis, both the unimodal and bimodal stationary PDFs of oscillator responses are obtained with the EPC method and Monte Carlo simulation. Compared with the simulation results, good agreement is achieved with the presented solution procedure in the case of the polynomial degree being 6, especially in the tail regions of the PDFs of the system responses.

Stochastic path summation with memory

2015 ◽  
Vol 36 ◽  
pp. 1560006
Author(s):  
Christopher C. Bernido ◽  
M. Victoria Carpio-Bernido
Keyword(s):  
Probability Density Function ◽  
Diffusion Equation ◽  
Stochastic Processes ◽  
White Noise ◽  
Probability Density ◽  
Density Function ◽  
Path Integral ◽  
Different Types ◽  
With Memory

Some classes of stochastic processes with memory properties are investigated by evaluating the probability density function as a white noise path integral. The corresponding modified diffusion equation for different types of memory behavior is then discussed.

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