Fractional Poisson process

About: Fractional Poisson process is a research topic. Over the lifetime, 868 publications have been published within this topic receiving 17858 citations.

Poisson, Dobinski, Rota and coherent states

Abstract: New q- Dobinski formula might also be interpreted as the average of specific q-powers of random variable X with the usual Poisson distribution.

Hybrid Poisson Processes with Fuzzy Rate

Abstract: Poisson processes, particularly the time-dependent extension, play important roles in reliability and risk analysis. It should be fully aware that the Poisson modeling in the current reliability engineering and risk analysis literature is merely an ideology under which the random uncertainty governs the phenomena. In other words, current Poisson Models generate meaningful results if randomness assumptions hold. However, the real world phenomena are often facing the co-existence reality and thus the probabilistic Poisson modeling practices may be very doubtful. In this paper, we define the random fuzzy Poisson process, explore the related average chance distributions, and propose a scheme for the parameter estimation and a simulation scheme as well. It is expecting that a foundational work can be established for Poisson random fuzzy reliability and risk analysis.

Poisson formula for a family of non-commutative Lobachevsky spaces

Abstract: We define an analog of the Poisson integral formula for a family of the non-commutative Lobachevsky spaces The q-Fourier transform of the Poisson kernel is expressed through the q-Bessel-Macdonald function