Markov models of non-Gaussian exponentially correlated processes and their applications

Primak, Serguei; Lyandres, V.; Kontorovich, Valeri

doi:10.1103/physreve.63.061103

Cited by 17 publications

(8 citation statements)

References 21 publications

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“…The method can also have engineering applications in the study of noise generators that asked the following question: Given an arbitrary probability density and a linear force (i.e., quadratic potential), how can we construct a Fokker-Planck equation such that the probability density is the stationary probability density of that equation? The Langevin equation of such a Fokker-Planck equation can then be used in engineering applications as noise generator for the desired probability density [33][34][35]. It would be interesting that a similar question can be addressed from two perspectives (this work and the work by Primak) which demand new attempts to study.…”

Section: Discussionmentioning

confidence: 97%

Families of Fokker-Planck equations and the associated entropic form for a distinct steady-state probability distribution with a known external force field

Asgarani

2015

Phys. Rev. E

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A method of finding entropic form for a given stationary probability distribution and specified potential field is discussed, using the steady-state Fokker-Planck equation. As examples, starting with the Boltzmann and Tsallis distribution and knowing the force field, we obtain the Boltzmann-Gibbs and Tsallis entropies. Also, the associated entropy for the gamma probability distribution is found, which seems to be in the form of the gamma function. Moreover, the related Fokker-Planck equations are given for the Boltzmann, Tsallis, and gamma probability distributions.

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Section: Discussionmentioning

confidence: 97%

Families of Fokker-Planck equations and the associated entropic form for a distinct steady-state probability distribution with a known external force field

Asgarani

2015

Phys. Rev. E

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“…Since the gamma distribution is defined only on the positive side of the real axis, this method is inappropriate. SDE-based process generation was addressed in [4], [5]; however, a significant part of the presented results was more theoretical than numerical. Davidson et.…”

Section: Introductionmentioning

confidence: 93%

“…Whenever the exponential autocorrelation function is required, f (x) and g(x) are given by [4,Eq. (48),(50)], [5] …”

Section: A Synthesis Of Sdementioning

confidence: 99%

Simple Generation of Gamma, Gamma–Gamma, and K Distributions With Exponential Autocorrelation Function

Bykhovsky

2016

J. Lightwave Technol.

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The simulation of a free-space optical (FSO) communication channel in the presence of strong turbulence typically requires the generation of channel states with a K or gammagamma distribution and a predefined autocorrelation function. In this paper we propose a simple and effective simulator of the strong-turbulence FSO channel that addresses the influence of the temporal covariance effect. Specifically, the proposed simulator provides K and gamma-gamma distributed values with the exponential autocorrelation function and a prescribed correlation time. This simulator is based on the numerical solution of the first-order stochastic differential equation (SDE). The simulated channel states are generated by a simple discrete-time differential equation and the simulator performance is analyzed in the paper.

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“…A characteristic feature of noise sources is that they are stationary. In view of this property, strongly nonlinear stochastic processes can be defined which for any initial probability density are stationary [147,189,190]. For example, the strongly nonlinear Langevin equation…”

Section: Engineering Sciencesmentioning

confidence: 99%

Strongly Nonlinear Stochastic Processes in Physics and the Life Sciences

Frank

2013

ISRN Mathematical Physics

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Strongly nonlinear stochastic processes can be found in many applications in physics and the life sciences. In particular, in physics, strongly nonlinear stochastic processes play an important role in understanding nonlinear Markov diffusion processes and have frequently been used to describe order-disorder phase transitions of equilibrium and nonequilibrium systems. However, diffusion processes represent only one class of strongly nonlinear stochastic processes out of four fundamental classes of time-discrete and time-continuous processes evolving on discrete and continuous state spaces. Moreover, strongly nonlinear stochastic processes appear both as Markov and non-Markovian processes. In this paper the full spectrum of strongly nonlinear stochastic processes is presented. Not only are processes presented that are defined by nonlinear diffusion and nonlinear Fokker-Planck equations but also processes are discussed that are defined by nonlinear Markov chains, nonlinear master equations, and strongly nonlinear stochastic iterative maps. Markovian as well as non-Markovian processes are considered. Applications range from classical fields of physics such as astrophysics, accelerator physics, order-disorder phase transitions of liquids, material physics of porous media, quantum mechanical descriptions, and synchronization phenomena in equilibrium and nonequilibrium systems to problems in mathematics,

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Markov models of non-Gaussian exponentially correlated processes and their applications

Cited by 17 publications

References 21 publications

Families of Fokker-Planck equations and the associated entropic form for a distinct steady-state probability distribution with a known external force field

Families of Fokker-Planck equations and the associated entropic form for a distinct steady-state probability distribution with a known external force field

Simple Generation of Gamma, Gamma–Gamma, and K Distributions With Exponential Autocorrelation Function

Strongly Nonlinear Stochastic Processes in Physics and the Life Sciences

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