Applications of inverse tempered stable subordinators

Rawashdeh, Mahmoud S.; Kelly, James Floyd; Meerschaert, Mark M.; Scheffler, Hans–Peter

doi:10.1016/j.camwa.2016.07.026

Cited by 52 publications

(34 citation statements)

References 48 publications

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“…with the same initial conditions as in Theorem 2, where the derivative in the l.h.s. is defined by (20), and h f (t, u) is now the density of the inverse tempered stable subordinator, the exact formula for which is presented, for example, in [2].…”

mentioning

confidence: 99%

On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators

Buchak

Sakhno

2019

Theor. Probability and Math. Statist.

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confidence: 99%

On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators

Buchak

Sakhno

2019

Theor. Probability and Math. Statist.

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“…with constants C, λ > 0 (see [6] and [58] One can weight differently the points in past or future depending on the present position, and one can also add a local part to complete the picture, leading to the operators…”

Section: Generalized Fractional Operators and Markov Processesmentioning

confidence: 99%

“…Therefore it is natural to modify the obtained CD-type derivatives by subtracting the killing term. In fact, performing thus procedure with the dressing by the exponential function e −λx leads to the tempered fractional derivatives defined by the Lévy kernel (2.21) (see [6] and [58]).…”

Section: Changing Variable Of Integration Yieldsmentioning

confidence: 99%

The Probabilistic Point of View on the Generalized Fractional Partial Differential Equations

Kolokoltsov

2019

FCAA

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This paper aims at unifying and clarifying the recent advances in the analysis of the fractional and generalized fractional Partial Differential Equations of Caputo and Riemann-Liouville type arising essentially from the probabilistic point of view. This point of view leads to the path integral representation for the solutions of these equations, which is seen to be stable with respect to the initial data and key parameters and is directly amenable to numeric calculations (Monte-Carlo simulation). In many cases these solutions can be compactly presented via the wide class of operator-valued analytic functions of the Mittag-Leffler type, which are proved to be expressed as the Laplace transforms of the exit times of monotone Markov processes.

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“…Such characteristic crossover from subdiffusion to normal diffusion has been observed also in lipid bilayer systems [ 56 , 57 , 58 ]. The tempered stable process in different guises has been intensively researched recently [ 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 ]. The aim of this work is to get the stochastic representation of anomalous diffusion tending to the confinement.…”

Section: Introductionmentioning

confidence: 99%

Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement

Stanislavsky

Weron

2020

Entropy

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The Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit theorem. Sums of Laplace distributed random variables are not Laplace distributed. We discovered a new mechanism leading to the Laplace distribution of observable values. This mechanism changes the contribution ratio between a jump and a continuous parts of random processes. Our concept uses properties of Bernstein functions and subordinators connected with them.

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Applications of inverse tempered stable subordinators

Cited by 52 publications

References 48 publications

On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators

On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators

The Probabilistic Point of View on the Generalized Fractional Partial Differential Equations

Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement

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