Nonlinear stochastic equations with multiplicative Lévy noise

Srokowski, T.

doi:10.1103/physreve.81.051110

Cited by 29 publications

(25 citation statements)

References 26 publications

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“…where dL(t) has the stable Lévy distribution [42]; then dη(t) is given by a limit of the vanishing relaxation time, dη(t) = lim γn→∞ dη c (t). The numerical analysis for the symmetric noise demonstrates [23,24] that results obtained by means of the variable transformation agree with those for the white noise in the Stratonovich interpretation. Then we solve the equationẏ…”

Section: Langevin Equationsupporting

confidence: 53%

“…Studies of the Langevin equation with the multiplicative Lévy noise [23,24] for the symmetric case demonstrate that physical conclusions qualitatively depend on a particular interpretation of the stochastic integral. The dynamics in the Stratonovich interpretation may be characterised by a finite variance, even in the absence of any potential, and then the solution exhibits fast falling power-law tails and a subdiffusive behaviour.…”

Section: Introductionmentioning

confidence: 99%

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Asymmetric Lévy flights in nonhomogeneous environments

Srokowski¹

2014

J. Stat. Mech.

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We consider stochastic systems involving general -non-Gaussian and asymmetric -stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A fractional diffusion equation corresponding to a master equation for a jumping process with a variable jumping rate is solved in a diffusion limit. It is demonstrated that for some model parameters the equation is satisfied in that limit by the stable process with the same asymptotics as the driving noise. The Langevin equation containing a multiplicative noise, depending on the position as a power-law, is solved; the existing moments are evaluated. The motion appears subdiffusive and the transport depends on the asymmetry parameter: it is fastest for the symmetric case. As a special case, the one-sided distribution is discussed.

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Section: Langevin Equationsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Asymmetric Lévy flights in nonhomogeneous environments

Srokowski¹

2014

J. Stat. Mech.

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“…MFPT monotonically rises with α for the symmetric noise if both a reflecting and absorbing barrier are assumed. Predictions of the Langevin equation with the multiplicative Lévy stable noise depend, in addition, on the parameter θ and on a specific interpretation of the stochastic integral [13,14]. MFPT initially falls with θ and then rises which behaviour means -for the Stratonovich interpretation -that the dependence on the effective barrier width is stronger than on the barrier height.…”

Section: Jumping Over a Potential Barriermentioning

confidence: 99%

Bistable generalised Langevin dynamics driven by correlated noise possessing a long jump distribution: barrier crossing and stochastic resonance

Srokowski

2013

Eur. Phys. J. B

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The generalised Langevin equation with a retarded friction and a double-well potential is solved. The random force is modelled by a multiplicative noise with long jumps. Probability density distributions converge with time to a distribution similar to a Gaussian but tails have a power-law form. Dependence of the mean first passage time on model parameters is discussed. Properties of the stochastic resonance, emerging as a peak in the plot of the spectral amplification against the temperature, are discussed for various sets of the model parameters. The amplification rises with the memory and is largest for the cases corresponding to the large passage time.

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“…(33). We evaluate the resulting Mellin transform and obtain the Fourier transform corresponding to the stable distribution for small |k|.…”

Section: A Multiplicative Noisementioning

confidence: 99%

Anomalous diffusion in stochastic systems with nonhomogeneously distributed traps

Srokowski

2015

Phys. Rev. E

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The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general Lévy stable statistics and experiences long rests due to nonhomogeneously distributed traps. The memory is taken into account by subordination of that process to a random time; then the subordination equation is position-dependent. The problem is approximated by a decoupling of the medium structure and memory and exactly solved for a power-law position dependence of the memory. In the case of the Gaussian statistics, the density distribution and moments are derived: depending on geometry and memory parameters, the system may reveal both the subdiffusion and enhanced diffusion. The similar analysis is performed for the Lévy flights where the finiteness of the variance follows from a variable noise intensity near a boundary. Two diffusion regimes are found: in the bulk and near the surface. The anomalous diffusion exponent as a function of the system parameters is derived.

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Nonlinear stochastic equations with multiplicative Lévy noise

Cited by 29 publications

References 26 publications

Asymmetric Lévy flights in nonhomogeneous environments

Asymmetric Lévy flights in nonhomogeneous environments

Bistable generalised Langevin dynamics driven by correlated noise possessing a long jump distribution: barrier crossing and stochastic resonance

Anomalous diffusion in stochastic systems with nonhomogeneously distributed traps

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