Theory for correlation functions of processes driven by external colored noise

Hernández–Machado, A.; Casademunt, Jaume; Rodríguez, Miguel A.; Pesquera, L.; Noriega, J. M.

doi:10.1103/physreva.43.1744

Cited by 21 publications

(10 citation statements)

References 19 publications

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“…The expression for the calculation of the correlation function of the non-Markovian process was obtained in [8,9]. In the short-time regime, it has the form…”

Section: Methods Of Calculation Of the Correlation Functionmentioning

confidence: 99%

“…The non-Markovian correlation function in the DE approximation is given by the expression [8,9] ( ) = 1 exp( 1 )+ 2 exp( 2 )+ (1− − / ) ) − . In these formulas, the relaxation rates are determined by expressions…”

Section: Methods Of Calculation Of the Correlation Functionmentioning

confidence: 99%

“…In the non-Markovian case, the dependence of the correlation function on noise parameters may have some specific features, as compared to the Markovian limit [2,6,7,8]. The generalization of the DE method to the case of a Gaussian colored noise in the first approximation with respect to the noise correlation time has been done in [2,9]. In particular, the connection between the non-Markovian correlation function ( ) and the effective Markovian correlation function has been established.…”

Section: Introductionmentioning

confidence: 99%

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Decay of Intensity Correlation Function near Instability Point for the Model of Resonant Tunneling

Ponezha¹

2016

Ukr. J. Phys.

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The decay of the correlation function ( ) of an electron flow intensity near an instability point for the process of resonant tunneling through a double barrier structure is considered. It is supposed that the intensity of the incoming flow may fluctuate under the influence of an external noise, both white and colored. The correlation function ( ) behavior is analyzed, by using methods leading to the single-exponential approximation such as the method of projection operator and the method of mean relaxation time. Moreover, the method based on a combination of high-and low-frequency expansions of the Laplace transform of ( ), which has allowed the correlation function to be approximated by two decaying exponentials, is applied. The numerical simulation has shown that the latter approach unlike the others gives correct results near the instability point. K e y w o r d s: resonant tunneling, intensity correlation function decay, instability point.

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“…The expression for the calculation of the correlation function of the non-Markovian process was obtained in [8,9]. In the short-time regime, it has the form…”

Section: Methods Of Calculation Of the Correlation Functionmentioning

confidence: 99%

Section: Methods Of Calculation Of the Correlation Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Decay of Intensity Correlation Function near Instability Point for the Model of Resonant Tunneling

Ponezha¹

2016

Ukr. J. Phys.

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“…Studies have confirmed the role of noise in nonlinear stochastic systems [1]. Now it has been realized that the effects of noise have widely appeared in all kinds of nonlinear systems including bistable systems [2][3][4][5], laser systems [6,7] and biological systems [8][9][10][11][12]. Some of the notable examples of noise induced effects are stochastic resonance in biological systems.…”

Section: Introductionmentioning

confidence: 95%

Dynamics of Gompertzian tumour growth under environmental fluctuations

Sahoo

Shearer

2010

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe investigate the effect of correlated additive and multiplicative Gaussian white noise on the Gompertzian growth of tumours. Our results are obtained by solving numerically the time-dependent Fokker-Planck equation (FPE) associated with the stochastic dynamics. In our numerical approach we have adopted B-spline functions as a truncated basis to expand the approximated eigenfunctions. The eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under study. We perform simulations to analyze various aspects, of the probability distribution, of the tumour cell populations in the transient-and steady-state regimes. More precisely, we are concerned mainly with the behaviour of the relaxation time (τ ) to the steady-state distribution as a function of (i) of the correlation strength (λ) between the additive noise and the multiplicative noise and (ii) as a function of the multiplicative noise intensity (D) and additive noise intensity (α). It is observed that both the correlation strength and the intensities of additive and multiplicative noise, affect the relaxation time.

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“…With regards to modeling studies on DNAPL degradation kinetics, very few of them attempted to address the resonance of their modeling results to potentially existing colored noise (Hernandez-Machado et al, 1991;Angulo et al, 2008;Durdu, 2010). Usually, colored noise can have effects on stochastic resonance in physical, chemical and biological and systems (Castro et al, 1995;Stijnen and Heemink, 2003).…”

Section: Introductionmentioning

confidence: 98%

Estimation of stochastic colored noise signal driving DNAPLs degradation kinetics in the natural water environment

2015

Chemosphere

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Theory for correlation functions of processes driven by external colored noise

Cited by 21 publications

References 19 publications

Decay of Intensity Correlation Function near Instability Point for the Model of Resonant Tunneling

Decay of Intensity Correlation Function near Instability Point for the Model of Resonant Tunneling

Dynamics of Gompertzian tumour growth under environmental fluctuations

Estimation of stochastic colored noise signal driving DNAPLs degradation kinetics in the natural water environment

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