Tempered fractional Langevin–Brownian motion with inverse<i>β</i>-stable subordinator

Chen, Yao; Wang, Xudong; Deng, Weihua

doi:10.1088/1751-8121/aae8b3

Cited by 21 publications

(21 citation statements)

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“…Due to the independence between the original process x(s) and the inverse subordinator s(t), the PDF p(x, t) can be written as [54][55][56][57] p(x, t)…”

Section: Random Diffusivity Model and Subordinatormentioning

confidence: 99%

Ergodic property of random diffusivity system with trapping events

Wang,

Chen

2021

Preprint

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Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous environment. This paper considers a Langevin system containing a random diffusivity and an α-stable subordinator with α < 1. This model describes the particle's motion in complex media where both the long trapping events and random diffusivity exist. We derive the general expressions of ensemble-and time-averaged mean-squared displacements which only contain the values of the inverse subordinator and diffusivity. Further taking specific time-dependent diffusivity, we obtain the analytic expressions of ergodicity breaking parameter and probability density function of the time-averaged mean-squared displacement. The results imply the nonergodicity of the random diffusivity model for any kind of diffusivity, including the critical case where the model presenting normal diffusion.

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“…Due to the independence between the original process x(s) and the inverse subordinator s(t), the PDF p(x, t) can be written as [54][55][56][57] p(x, t)…”

Section: Random Diffusivity Model and Subordinatormentioning

confidence: 99%

Ergodic property of random diffusivity system with trapping events

Wang,

Chen

2021

Preprint

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“…Next, we introduce the infinite dimensional tempered fractional Gaussian noise. The tfBm, describing anomalous diffusion with exponentially tempered long range correlations, was introduced in [5,22] with its definition…”

Section: Notations and Preliminariesmentioning

confidence: 99%

“…Considering the fickle natural environment, sometimes the stochastic disturbance of the source can not be ignored. The 'localization' is one of the typical properties of fluctuation, well modeled by the tempered fractional Brownian motion (tfBm) [5,22]. The model we discuss in this paper is Eq.…”

Section: Introductionmentioning

confidence: 99%

Numerical approximation for fractional diffusion equation forced by a tempered fractional Gaussian noise

Liu,

Deng

2019

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This paper discusses the fractional diffusion equation forced by a tempered fractional Gaussian noise. The fractional diffusion equation governs the probability density function of the subordinated killed Brownian motion. The tempered fractional Gaussian noise plays the role of fluctuating external source with the property of localization. We first establish the regularity of the infinite dimensional stochastic integration of the tempered fractional Brownian motion and then build the regularity of the mild solution of the fractional stochastic diffusion equation. The spectral Galerkin method is used for space approximation; after that the system is transformed into an equivalent form having better regularity than the original one in time. Then we use the semi-implicit Euler scheme to discretize the time derivative. In terms of the temporal-spatial error splitting technique, we obtain the error estimates of the fully discrete scheme in the sense of mean-squared L 2 -norm. Extensive numerical experiments confirm the theoretical estimates.

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“…More precisely, TFGN can provide a useful stochastic process model for wind speed data, see, e.g., [3,10,17,23,29]. Furthermore, the time-changed TFBM has been investigated in [9] with potential applications in financial time series, biology and physics.…”

Section: Introductionmentioning

confidence: 99%

Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

2021

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In this paper we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion B σ,λ Q (t) with −1/2 < σ < 0 and λ > 0. We first introduce a technical lemma which is crucial in our stability analysis. Then we prove the existence and uniqueness of mild solutions by using semigroup methods. The upper nonlinear noise excitation index of the energy solutions at any finite time t is also obtained. Finally, we consider the exponential asymptotic behavior of mild solutions in mean square.

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Tempered fractional Langevin–Brownian motion with inverseβ-stable subordinator

Cited by 21 publications

References 50 publications

Ergodic property of random diffusivity system with trapping events

Ergodic property of random diffusivity system with trapping events

Numerical approximation for fractional diffusion equation forced by a tempered fractional Gaussian noise

Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

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