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of 135
pro vyhledávání: '"Baeumer, Boris"'
Univariate marked Hawkes processes are used to model a range of real-world phenomena including earthquake aftershock sequences, contagious disease spread, content diffusion on social media platforms, and order book dynamics. This paper illustrates a
Externí odkaz:
http://arxiv.org/abs/2407.03619
Most point process models for earthquakes currently in the literature assume the magnitude distribution is i.i.d. potentially hindering the ability of the model to describe the main features of data sets containing multiple earthquake mainshock after
Externí odkaz:
http://arxiv.org/abs/2404.01478
This paper extends the existing fractional Hawkes process to better model mainshock-aftershock sequences of earthquakes. The fractional Hawkes process is a self-exciting point process model with temporal decay kernel being a Mittag-Leffler function.
Externí odkaz:
http://arxiv.org/abs/2403.00142
We develop a finite difference approximation of order $\alpha$ for the $\alpha$-fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Gr\"unwald scheme. In particular, approximate solu
Externí odkaz:
http://arxiv.org/abs/2112.08529
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting the model
Externí odkaz:
http://arxiv.org/abs/2103.00715
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting the model
Externí odkaz:
http://arxiv.org/abs/2012.10864
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Akademický článek
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This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solu
Externí odkaz:
http://arxiv.org/abs/1706.07991
Publikováno v:
Journal of Differential Equations 264 (2018), 1377-1410
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show well-posednes
Externí odkaz:
http://arxiv.org/abs/1706.07266