Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion

Wyłomańska, Agnieszka; Kumar, Arun; Połoczański, Rafał; Vellaisamy, P.

doi:10.1103/physreve.94.042128

Cited by 21 publications

(9 citation statements)

References 46 publications

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“…The simulation procedures for sample paths (or trajectories) of subordinated processes have been widely described in the literature, for example FBM time-changed by gamma subordinator is discussed in Kozubowski et al (2006) and FBM time-changed by Inverse Gaussian subordinator is analyzed in Wyłomańska et al (2016). The main idea is to simulate independent trajectories of the subordinator S λ,α (t) and the FBM B H (t).…”

Section: Fbm Delayed By Tempered Stable Subordinatormentioning

confidence: 99%

Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators

Kumar

Gajda

Wyłomańska

et al. 2018

Methodol Comput Appl Probab

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In recent years subordinated processes have been widely considered in the literature. These processes not only have wide applications but also have interesting theoretical properties. In this paper we consider fractional Brownian motion (FBM) time-changed by two processes, tempered stable and inverse tempered stable. We present main properties of the subordinated FBM such as long range dependence and associated fractional partial differential equations for the probability density functions. Moreover, we present how to simulate both subordinated processes.

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Section: Fbm Delayed By Tempered Stable Subordinatormentioning

confidence: 99%

Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators

Kumar

Gajda

Wyłomańska

et al. 2018

Methodol Comput Appl Probab

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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%

Lévy-walk-like Langevin dynamics

2019

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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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“…Barndorff-Nielsen points out that the mixture of the normal distribution and the generalized inverse Gaussian distribution is just the generalized hyperbolic distribution [36,37]. The generalized inverse Gaussian distribution appears in for example fractional Brownian motion [38] and inverse Ising problem [39].…”

Section: Generalized Inverse Gaussian Distributionmentioning

confidence: 99%

Probability Thermodynamics and Probability Quantum Field

Zhang,

Li,

Liu

et al. 2019

Preprint

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In this paper, we introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define spectral functions. Various thermodynamic quantities in thermodynamics and effective actions in quantum field theory are all spectral functions. In the scheme, eigenvalues obey a probability distribution, so a probability distribution determines a family of spectral functions in thermodynamics and in quantum field theory. This leads to probability thermodynamics and probability quantum fields determined by a probability distribution. There are two types of spectra: lower bounded spectra, corresponding to the probability distribution with nonnegative random variables, and the lower unbounded spectra, corresponding to probability distributions with negative random variables. For lower unbounded spectra, we use the generalized definition of spectral functions. In some cases, we encounter divergences. We remove the divergence by a renormalization procedure. Moreover, in virtue of spectral theory in physics, we generalize some concepts in probability theory. For example, the moment generating function in probability theory does not always exist. We redefine the moment generating function as the generalized heat kernel, which makes the concept definable when the definition in probability theory fails. As examples, we construct examples corresponding to some probability distributions. Thermodynamic quantities, vacuum amplitudes, one-loop effective actions, and vacuum energies for various probability distributions are presented.

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Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion

Cited by 21 publications

References 46 publications

Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators

Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators

Lévy-walk-like Langevin dynamics

Probability Thermodynamics and Probability Quantum Field

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