Stable Lévy motion with inverse Gaussian subordinator

Kumar, Arun; Wyłomańska, Agnieszka; Gajda, Janusz

doi:10.1016/j.physa.2017.04.097

Cited by 4 publications

(4 citation statements)

References 44 publications

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“…More kinds of subordinators (e.g. tempered stable, gamma, inverse Gaussian, and inverse inverse Gaussian subordinators) are considered in [48][49][50][51]. The (two-point) PDFs of inverse subordinator s(t) in (10) and (11) can be directly applied to other inverse subordinators for a specific Φ(λ).…”

Section: T S Smentioning

confidence: 99%

“…The α 0 -stable subordinator for 0 < α 0 < 1 is commonly used in Langevin system to describe subdiffusion in [7,27] or superdiffusion in [29,44]. More kinds of subordinators (e.g., tempered stable, gamma, inverse Gaussian, and inverse inverse Gaussian subordinators) are considered in [45,46,47,48]. The (two-point) PDFs of inverse subordinator s(t) in (10) and (11) can be directly applied to other inverse subordinators for a specific Φ(λ).…”

Section: Pdfs Of α-Dependent Subordinator (1 < α < 2) and Its Inverse...mentioning

confidence: 99%

“…This is the fractional Klein-Kramers equation governing the joint PDF of positionvelocity of the Langevin system (48). Note that in this case, the Newton relation does not hold between x(t) and v(t) and Galilean invariance is violated [6,64].…”

Section: Comparison With Another Langevin Systemmentioning

confidence: 99%

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Lévy-walk-like Langevin dynamics

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Continuous-time random walks and Langevin equations are two classes of stochastic models used to describe the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more often one model has significant advantages (or has to be used) compared with the other one. In this paper, we consider the weakly damped Langevin system coupled with a new subordinator-α-dependent subordinator with 1<α<2. We pay attention to the diffusive behavior of the stochastic process described by this coupled Langevin system, and find the super-ballistic diffusion phenomenon for the system with an unconfined potential on velocity but sub-ballistic superdiffusion phenomenon with a confined potential, which is like Lévy walk for long times. One can further note that the two-point distribution of inverse subordinator affects mean square displacement of this coupled weakly damped Langevin system in essential. 0 , model (1) yields subdiffusion. Nowadays, subordinator is a very effective tool to characterize various complex dynamical systems, especially some real-life data in biology [8]

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Section: T S Smentioning

confidence: 99%

Section: Pdfs Of α-Dependent Subordinator (1 < α < 2) and Its Inverse...mentioning

confidence: 99%

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Lévy-walk-like Langevin dynamics

2019

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“…The reader can also consult, for instance, refs. [16][17][18][19][20][21][22][23] for more information on this topic.…”

Section: Introductionmentioning

confidence: 99%

Hadamard-Type Fractional Heat Equations and Ultra-Slow Diffusions

Gregorio

Garra

2021

Fractal Fract

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In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the Hadamard operator. The stochastic meaning of the introduced abstract differential equation is provided, and the application to the particular case of the fractional heat equation is then discussed in detail. The ultra-slow behaviour emerges from the explicit form of the variance of the random process arising from our analysis. Finally, we obtain a particular solution for the nonlinear Hadamard-diffusive equation.

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Subordinated Processes with Infinite Variance

Grzesiek

Wyłomańska

2019

Applied Condition Monitoring

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Stable Lévy motion with inverse Gaussian subordinator

Cited by 4 publications

References 44 publications

Lévy-walk-like Langevin dynamics

Lévy-walk-like Langevin dynamics

Hadamard-Type Fractional Heat Equations and Ultra-Slow Diffusions

Subordinated Processes with Infinite Variance

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