Non-homogeneous space-time fractional Poisson processes

References

• Leonenko, N., Scalas, E., Trinh, M. (2017). The fractional non-homogeneous Poisson process. Statist. Probab. Lett. 120:147–156.
   Web of Science ®Google Scholar
• Laskin, N. (2003). Fractional Poisson process. Chaotic transport and complexity in classical and quantum dynamics. Commun. Nonlinear Sci. Numer. Simul. 8(3–4):201–213.
   Web of Science ®Google Scholar
• Orsingher, E., Polito, F. (2012). The space-fractional Poisson process. Statist. Probab. Lett. 82(4):852–858.
   Web of Science ®Google Scholar
• Aletti, G., Leonenko, N., Merzbach, E. (2018). Fractional Poisson fields and martingales. J. Stat. Phys. 170(4):700–730.
   Web of Science ®Google Scholar
• Mittag-Leffler, G. (1903). Sur la nouvelle fonction eα(x). C. R. Acad. Sci. Paris 137:554–558.
   Google Scholar
• Gorenflo, R., Mainardi, F. (2013). On the fractional Poisson process and the discretized stable subordinator. Submitted. arXiv:1305.3074 [math.PR].
   Google Scholar
• Mainardi, F. (2010). Fractional Calculus and Waves in Linear Viscoelasticity. An Introduction to Mathematical Models. London: Imperial College Press.
   Google Scholar
• Applebaum, D. (2009). Lévy Processes and Stochastic Calculus, Volume 116 of Cambridge Studies in Advanced Mathematics, 2nd ed. Cambridge: Cambridge University Press.
   Google Scholar
• Bingham, N. H. (1971). Limit theorems for occupation times of Markov processes. Z Wahrscheinlichkeitstheorie Verw. Gebiete 17:1–22.
   Web of Science ®Google Scholar
• Meerschaert, M. M., Straka, P. (2013). Inverse stable subordinators. Math. Model. Nat. Phenom. 8(2):1–16.
   PubMed Web of Science ®Google Scholar
• Meerschaert, M. M., Scheffler, H.-P. (2004). Limit theorems for continuous-time random walks with infinite mean waiting times. J. Appl. Probab. 41(3):623–638.
   Web of Science ®Google Scholar
• Vellaisamy, P., Maheshwari, A. (2018). Fractional negative binomial and Polya processes. Probab. Math. Statist. 38(1):77–101.
   Web of Science ®Google Scholar
• D’Ovidio, M., Nane, E. (2014). Time dependent random fields on spherical non-homogeneous surfaces. Stochastic Process. Appl. 124(6):2098–2131.
   Web of Science ®Google Scholar
• Maheshwari, A., Vellaisamy, P. (2016). On the long-range dependence of fractional Poisson and negative binomial processes. J. Appl. Probab. 53:989–1000.
   Web of Science ®Google Scholar
• Kilbas, A. A., Srivastava, H. M., Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations, Volume 204 of North-Holland Mathematics Studies. Amsterdam: Elsevier Science B.V.
   Google Scholar
• Zacks, S. (2004). Distributions of failure times associated with non-homogeneous compound Poisson damage processes. In: A Festschrift for Herman Rubin, Volume 45 of IMS Lecture Notes Monograph Series, pp. 396–407. Beachwood, OH: Institute of Mathematical Statistics.
   Google Scholar
• Basu, A. P., Rigdon, S. E. (2001). Ch. 2. The Weibull nonhomogeneous Poisson process. In: Advances in Reliability, Volume 20 of Handbook of Statistics. New York: Elsevier, pp. 43–68.
   Google Scholar
• Hee-Cheul, K., Kyung-Soo, K. (2015). Software development cost model based on NHPP Gompertz distribution. Indian J. Sci. Technol. 8(12). DOI:10.17485/ijst/2015/v8i12/68332
   Google Scholar
• Ohishi, K., Okamura, H., Dohi, T. (2009). Gompertz software reliability model: Estimation algorithm and empirical validation. J. Syst. Softw. 82(3):535–543.
   Web of Science ®Google Scholar
• Tae-Hyun, Y. (2015). The infinite NHPP software reliability model based on monotonic intensity function. Indian J. Sci. Technol. 8(14). DOI:10.17485/ijst/2015/v8i14/68342
   Google Scholar
• Bertoin, J. (1996). Lévy Processes, Volume 121 of Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press.
   Google Scholar
• Beghin, L., Orsingher, E. (2009). Fractional Poisson processes and related planar random motions. Electron. J. Probab. 14(61):1790–1827.
   Google Scholar
• Leonenko, N. N., Meerschaert, M. M., Schilling, R. L., Sikorskii, A. (2014). Correlation structure of time-changed Lévy processes. Commun. Appl. Ind. Math. 6(1):e483.
   Web of Science ®Google Scholar
• Cahoy, D. O., Uchaikin, V. V., Woyczynski, W. A. (2010). Parameter estimation for fractional Poisson processes. J. Statist. Plann. Inference 140(11):3106–3120.
   Web of Science ®Google Scholar
• Kanter, M. (1975). Stable densities under change of scale and total variation inequalities. Ann. Probab. 3(4):697–707.
   Web of Science ®Google Scholar
• Maheshwari, A., Vellaisamy, P. Fractional Poisson process time-changed by Lévy subordinator and its inverse. J. Theor. Probab. DOI:10.1007/s10959-017-0797-6
   Google Scholar