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Non-homogeneous space-time fractional Poisson processes
, Vellaisamy P
Published in Taylor and Francis
Volume: 37
Issue: 2
Pages: 137 - 154

The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto (2012), is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional generalization of the non-homogeneous Poisson process and call it the non-homogeneous space-time fractional Poisson process (NHSTFPP). We compute their pmf and generating function and investigate the associated differential equation. The limit theorems for the NHSTFPP process are studied. We study the distributional properties, the asymptotic expansion of the correlation function of the non-homogeneous time fractional Poisson process (NHTFPP) and subsequently investigate the long-range dependence (LRD) property of a special NHTFPP. We investigate the limit theorem for the fractional non-homogeneous Poisson process (FNHPP) studied by Leonenko et al. (2014). Finally, we present some simulated sample paths of the NHSTFPP process.

About the journal
JournalData powered by TypesetStochastic Analysis and Applications
PublisherData powered by TypesetTaylor and Francis
Open AccessYes
Concepts (4)
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    Probability and uncertainty
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    Statistics and probability
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    Applied mathematics