Ideal and physical barrier problems for non-linear systems driven by normal and Poissonian white noise via path integral method

2016 ◽  
Vol 81 ◽  
pp. 274-282 ◽  
Author(s):  
Mario Di Paola ◽  
Christian Bucher
Keyword(s):  
White Noise ◽  
Linear Systems ◽  
Path Integral ◽  
Integral Method ◽  
Physical Barrier ◽  
Non Linear ◽  
Non Linear Systems ◽  
Path Integral Method ◽  
Barrier Problems

Measurement of Wiener kernels

1984 ◽  
Vol 16 (1) ◽  
pp. 11-12
Author(s):  
Yoshifusa Ito
Keyword(s):  
Differential Operator ◽  
Mathematical Models ◽  
White Noise ◽  
Linear Systems ◽  
Main Part ◽  
The Other ◽  
Linear Functionals ◽  
Wiener Kernels ◽  
Non Linear ◽  
Non Linear Systems

Since the late 1960s Wiener's theory on the non-linear functionals of white noise has been widely applied to the construction of mathematical models of non-linear systems, especially in the field of biology. For such applications the main part is the measurement of Wiener's kernels, for which two methods have been proposed: one by Wiener himself and the other by Lee and Schetzen. The aim of this paper is to show that there is another method based on Hida's differential operator.

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Mario Di Paola ◽  
Gioacchino Alotta
Keyword(s):  
Path Integral ◽  
Path Integration ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Kolmogorov Equation ◽  
Integral Methods ◽  
Alternative Approach ◽  
Path Integration Method ◽  
Path Integral Method ◽  
Barrier Problems

Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is analyzed. Lastly, an alternative approach to the path integration method, that is the Wiener Path integration (WPI), also based on the Chapman–Komogorov equation, is discussed. The main advantages and the drawbacks in using these two methods are deeply analyzed and the main results available in literature are highlighted.

First-passage problem for nonlinear systems under Lévy white noise through path integral method

2016 ◽  
Vol 85 (3) ◽  
pp. 1445-1456 ◽  
Author(s):  
Christian Bucher ◽  
Alberto Di Matteo ◽  
Mario Di Paola ◽  
Antonina Pirrotta
Keyword(s):  
Nonlinear Systems ◽  
White Noise ◽  
Path Integral ◽  
Integral Method ◽  
First Passage ◽  
Lévy White Noise ◽  
Path Integral Method ◽  
First Passage Problem
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