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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 +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 +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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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. +1 more
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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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NON-CONVEX HYBRID TOTAL VARIATION FOR RESTORING MEDICAL IMAGE CORRUPTED BY POISSON NOISE [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2023 In this work, we proposed the hybrid non-convex regularizers for Poisson noise removal on medical images. The model is built by a combination of non-convex total variation and non-convex fractional total variation.
T. T. T. Tran +5 more
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