Path Integral Method for Nonlinear Systems Under Levy White Noise

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Alberto Di Matteo ◽  
Antonina Pirrotta
Keyword(s):  
Probability Density Function ◽  
Nonlinear Systems ◽  
Probability Density ◽  
Density Function ◽  
Path Integral ◽  
Response Probability ◽  
Stability Index ◽  
Integral Solution ◽  
Stable Random Variables ◽  
White Noises

In this paper, the probabilistic response of nonlinear systems driven by alpha-stable Lévy white noises is considered. The path integral solution is adopted for determining the evolution of the probability density function of nonlinear oscillators. Specifically, based on the properties of alpha-stable random variables and processes, the path integral solution is extended to deal with Lévy white noises input with any value of the stability index alpha. It is shown that at the limit when the time increments tend to zero, the Einstein–Smoluchowsky equation, governing the evolution of the response probability density function, is fully restored. Application to linear and nonlinear systems under different values of alpha is reported. Comparisons with pertinent Monte Carlo simulation data and analytical solutions (when available) demonstrate the accuracy of the results.

scholarly journals Assessment of a three-dimensional line-of-response probability density function system matrix for PET

2012 ◽  
Vol 57 (21) ◽  
pp. 6827-6848 ◽  
Author(s):  
Rutao Yao ◽  
Ranjith M Ramachandra ◽  
Neeraj Mahajan ◽  
Vinay Rathod ◽  
Noel Gunasekar ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Three Dimensional ◽  
Response Probability ◽  
Function System ◽  
System Matrix

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.

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.

Sign in / Sign up

Export Citation Format

Share Document