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Mixingale estimation function for mixed fractional SPDEs with random effect and random sampling [PDF]

European Journal of Mathematics and Applications, 2022
We study the mixingale estimation function estimator of the parameters in the fractional stochastic partial differential equation when the process is observed at the arrival times of a Poisson process with the presence of random effect.
Jaya P. N. Bishwal
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A New Fractional Poisson Process Governed by a Recursive Fractional Differential Equation

Fractal and Fractional, 2022
This paper proposes a new fractional Poisson process through a recursive fractional differential governing equation. Unlike the homogeneous Poison process, the Caputo derivative on the probability distribution of k jumps with respect to time is linked to
Zhehao Zhang
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Some Compound Fractional Poisson Processes

Fractal and Fractional, 2022
In this paper, we introduce and study fractional versions of the Bell–Touchard process, the Poisson-logarithmic process and the generalized Pólya–Aeppli process.
Mostafizar Khandakar, Kuldeep Kumar Kataria   +1 more
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Non-Local Seismo-Dynamics: A Fractional Approach

Fractal and Fractional, 2022
This paper consists of a general consideration of a seismic system as a subsystem of another, larger system, exchanging with it by extensive dynamical quantities in a sequential push mode.
Vladimir Uchaikin, Elena Kozhemiakina
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Quasi-likelihood Estimation in Fractional Levy SPDEs from Poisson Sampling

European Journal of Mathematical Analysis, 2022
We study the quasi-likelihood estimator of the drift parameter in the stochastic partial differential equations driven by a cylindrical fractional Levy process when the process is observed at the arrival times of a Poisson process.
Jaya P. N. Bishwal
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Fractional Model of the Deformation Process

Fractal and Fractional, 2022
The article considers the fractional Poisson process as a mathematical model of deformation activity in a seismically active region. The dislocation approach is used to describe five modes of the deformation process.
Olga Sheremetyeva, Boris Shevtsov
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Biased Continuous-Time Random Walks with Mittag-Leffler Jumps

Fractal and Fractional, 2020
We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions.
Thomas M. Michelitsch, Federico Polito, Alejandro P. Riascos   +2 more
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Fractional Criticality Theory and Its Application in Seismology

Fractal and Fractional, 2023
To understand how the temporal non-locality («memory») properties of a process affect its critical regimes, the power-law compound and time-fractional Poisson process is presented as a universal hereditary model of criticality.
Boris Shevtsov, Olga Sheremetyeva
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Skellam Type Processes of Order k and Beyond

Entropy, 2020
In this article, we introduce the Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular, we discuss the space-fractional Skellam process and tempered space-fractional Skellam ...
Neha Gupta, Arun Kumar, Nikolai Leonenko
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Аппроксимация законов распределения времён ожидания форшоков на основе дробной модели деформационной активности

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022
В статье рассматриваются два алгоритма построения последовательностей форшоков, связанных с главным событием заданной энергии, на основе ранее разработанной авторами статистической модели деформационного процесса.
Шереметьева, О.В., Шевцов, Б.М.   +1 more
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