On martingale characterizations for some generalized space fractional Poisson processes

ABSTRACT

We obtain martingale characterizations for the generalized space fractional Poisson process (GSFPP) and for counting processes with Bernštein intertimes. These serve as extensions of the Watanabe's characterization for the classical homogenous Poisson process. The corresponding assertion for the space fractional Poisson process (SFPP) is obtained as a particular case of our results.

KEYWORDS:

• Martingale
• subordinators
• hitting times
• generalized space fractional Poisson processes

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G22
• 60G44

Acknowledgments

The authors would like to thank the anonymous reviewer for providing some useful comments on the initial version of the manuscript. The first author acknowledges the financial support from IRCC, IIT Bombay.

Additional information

Funding

The first author acknowledges the financial support from IRCC, IIT Bombay.