Journal ArticleDOI
Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process
TLDR
In this paper, the exact stationary solution in terms of probability density function for a restricted class of nonlinear systems under both external and parametric non-normal delta-correlated processes is presented.Abstract:
In this paper the exact stationary solution in terms of probability density function for a restricted class of non-linear systems under both external and parametric non-normal delta-correlated processes is presented. This class has been obtained by imposing a given probability distribution and finding the corresponding dynamical system which satisfies the modified Fokker-Planck equation. The effectiveness of the results has been verified by means of a Monte Carlo simulation.read more
Citations
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Path integral solution for non-linear system enforced by Poisson White Noise
M. Di Paola,Roberta Santoro +1 more
TL;DR: In this paper, a path integral solution for non-linear systems under Poisson white noise is presented, which may be considered as a step-by-step solution technique in terms of probability density function.
Journal ArticleDOI
Response of stochastic dynamical systems driven by additive Gaussian and Poisson white noise : Solution of a forward generalized Kolmogorov equation by a spectral finite difference method
TL;DR: In this paper, a numerical method is given for the solution of the probability density function of the response process of memoryless one-and two-state dynamical systems having polynomial restoring forces and which are subjected to a combination of Gaussian and Poisson white noises.
Journal ArticleDOI
Probabilistic response of nonlinear systems under combined normal and Poisson white noise via path integral method
TL;DR: In this paper, the response in terms of probability density function of nonlinear systems under combined normal and Poisson white noise is considered via a Path Integral Solution (PIS) that may be considered as a step-by-step solution technique.
Journal ArticleDOI
Exact stationary probability density functions for non-linear systems under Poisson white noise excitation
TL;DR: In this paper, the exact stationary probability density functions for systems under Poisson white noise excitation were derived for a class of non-linear systems whose state vector is a memoryless transformation of the state vector of a linear system.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
Brownian motion in a field of force and the diffusion model of chemical reactions
TL;DR: In this article, a particle which is caught in a potential hole and which, through the shuttling action of Brownian motion, can escape over a potential barrier yields a suitable model for elucidating the applicability of the transition state method for calculating the rate of chemical reactions.