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Fractional Risk Process in Insurance
Important models in insurance, for example the Carmér--Lundberg theory a...
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Parameter estimation for fractional Poisson processes
The paper proposes a formal estimation procedure for parameters of the f...
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On the fractional queueing model with catastrophes
Customers arrive at a service facility according to a Poisson process. U...
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Generating Sparse Stochastic Processes Using Matched Splines
We provide an algorithm to generate trajectories of sparse stochastic pr...
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Some characterisation results on classical and free Poisson thinning
Poisson thinning is an elementary result in probability, which is of gre...
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Entropic Compressibility of Lévy Processes
In contrast to their seemingly simple and shared structure of independen...
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Inference for Continuous Time Random Maxima with Heavy-Tailed Waiting Times
In many complex systems of interest, inter-arrival times between events ...
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Fractional Poisson Processes of Order K
In this article, we introduce and study time- and space-fractional Poisson processes of order k. These processes are defined in terms of fractional compound Poisson processes. Time-fractional Poisson process of order k naturally generalizes the Poisson process and Poisson process of order k to a heavy tailed waiting times counting process. The space-fractional Poisson process of order k, allows on average infinite number of arrivals in any interval. We derive the marginal probabilities, governing difference-differential equations of the introduced processes.
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