Journal ArticleDOI
The probability density and level-crossings of first-order non-linear systems driven by the random telegraph signal†
TLDR
Using extended forms of the Fokker-Planck-Kolmogorov equation, the so-called vth-order equations, a general expression is derived for p(y) and some specific eases are investigated, which are applied to find the average number of zero and level-crossings per unit time of the output process.Abstract:
We consider the probability density function p(y) of the output y(t) of the first-order non linear system [ydot] + β ƒ(y) = βx, where x = x(t) is the random telegraph signal and ƒ(·) is a non-linear function Employing extended forms of the Fokker-Planck-Kolmogorov equation, the so-called vth-order equations, a general expression is derived for p(y) and some specific eases are investigated These results are applied to find the average number of zero and level-crossings per unit time of the output processread more
Citations
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Journal ArticleDOI
Statistical properties of the asymmetric random telegraph signal, with applications to single-channel analysis
TL;DR: This collection of results includes both previously published formulas, here presented in most general form and in uniform notation, and some new results not previously published.
Journal ArticleDOI
Coloured-noise-induced transitions: Exact results for external dichotomous Markovian noise
TL;DR: In this article, a general method to calculate explicitly the stationary probability of nonlinear systems subjected to a special case of coloured noise is presented, for a simple model system the phase diagram for the various noise-induced transitions is determined.
Book ChapterDOI
A Survey of Recent Progress on Level-Crossing Problems for Random Processes
TL;DR: The present survey is intended to be an update of Blake and Lindsey’s survey of results and techniques for level-crossing problems for random processes with an emphasis on explicit analytical results for continuous parameter processes.
Journal ArticleDOI
On filtered binary processes
R. Pawula,S. Rice +1 more
TL;DR: The problem of calculating the probability density function of the output of an RC filter driven by a binary random process with intervals generated by an equilibrium renewal process is studied.
Journal ArticleDOI
A perturbation expansion for external wide band Markovian noise: Application to transitions induced by Ornstein-Uhlenbeck noise
Werner Horsthemke,René Lefever +1 more
TL;DR: In this paper, the stationary probability density of non-equilibrium systems subjected to wide band external colored noise is calculated by a systematic perturbation expansion in terms of the correlation time of the noise.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Journal ArticleDOI
Analysis of nonlinear stochastic systems by means of the Fokker–Planck equation†
TL;DR: In this article, a simplified derivation of the Fokker-Planck equation is given and the uniqueness of the steady-state solution for certain classes of system is discussed.
Journal ArticleDOI
Generalizations and extensions of the Fokker- Planck-Kolmogorov equations
TL;DR: The classical Fokker-Planck-Kolmogorov equations are generalized to hold for conditional probability density functions of arbitrary random processes both for one-dimensional and for vector random processes.
Journal ArticleDOI
Analysis of a Nonlinear First‐Order System with a White Noise Input
Thomas K. Caughey,J. K. Dienes +1 more
TL;DR: In this paper, a general technique for computing the power spectrum of nonlinear systems is presented, and the method is applied to the Brownian motion of a particle with idealized Coulomb damping.
Journal ArticleDOI
Probability Densities of the Smoothed ‘ Random Telegraph Signal ’†
W. M. Wonham,A. T. Fuller +1 more
TL;DR: The moments of the first probability distribution are obtained and the density function derived and the results suggest a convenient experimental method for generating low frequency noise with Gaussian, rectangular, parabolic or elliptical probability density functions.