Presented by: 
Nikolai Leonenko (Cardiff University)
Date: 
Mon 12 Sep, 2:00 pm - 3:00 pm
Venue: 
Mansergh Shaw building (45), room 204

We present new properties for the Fractional Poisson process [2,6], Fractional non-homogeneous Poisson process [5] and the Fractional Poisson fields on the plane [3]. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields, obtaining some other characterizations. The fractional differential equations are studied. The covariance structure is given. Finally, we give some simulations of the Fractional Poisson fields on the plane. Joint work with G. Aletti (University of Milan, Italy) and E. Merzbach (Bar Ilan University, Israel).

References:

[1] Aletti, G., Leonenko, N.N. and Marzbach, E. (2016) Fractional Poisson fields and martingales, submitted, http://arxiv.org/pdf/1601.08136.pdf

[2] Beghin,L. and E. Orsingher, E. (2009) Fractional Poisson processes and related planar random motions, Electron. J. Probab. 14, no. 61, 1790--1827.

[3] Leonenko, N.N. and Merzbach, E.(2015) Fractional Poisson fields, Methodology and Computing in Applied Probability, 17, 155-168

[4] Leonenko, N.N., Meerschaert, M.M., Schilling, R.L. and Sikorskii, A. (2014) Correlation structure of time-changed Lévy processes, Commun. Appl. Ind. Math. 6, no. 1, e-483, 22 pp.

[5] Leonenko, N., Scalas, E. and Trinh, M. (2016) The fractional non-homogeneous Poisson process, submitted, http://arxiv.org/abs/1601.03965 .

[6] Meerschaert, M.M., E. Nane, E., and P. Vellaisamy, P. (2011) The fractional Poisson process and the inverse stable subordinator, Electron. J. Probab. 16, no. 59, 1600-1620.