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Convoluted fractional Poisson process of order k.
- Source :
-
Stochastics: An International Journal of Probability & Stochastic Processes . Nov2023, Vol. 95 Issue 7, p1170-1191. 22p. - Publication Year :
- 2023
-
Abstract
- In this article, we define a convoluted fractional Poisson process of order k (CFPPoK), which is governed by the discrete convolution operator in the system of fractional differential equations. Next, we obtain its one-dimensional distribution by using the Laplace transform of its state probabilities. Various distributional properties, such as probability generating function, moment generating function and moments, are derived. A special case of CFPPoK, (say) convoluted Poisson process of order k (CPPoK) is studied and also established Martingale characterization for CPPoK. We further derive the covariance structure of CFPPoK and investigate the long-range dependence property. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17442508
- Volume :
- 95
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Stochastics: An International Journal of Probability & Stochastic Processes
- Publication Type :
- Academic Journal
- Accession number :
- 170717549
- Full Text :
- https://doi.org/10.1080/17442508.2023.2165399