Fractional Skellam Random Fields on ℝ²₊

2025/09/13 by Vishwakarma, Pradeep
#60G55 #60G60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.10870

Abstract

We study a Skellam point process on ℝ^M₊, M≥1. For M=2, it reduces to a Skellam random field on plane which is a two parameter Lévy process with rectangular increment. A weak convergent result is obtained for it. Further, we consider three fractional variants of Skellam random field on positive quadrant of plane. Their point probabilities, associated governing equations, and other distributional properties are studied in detail. Later, we consider an integral of Skellam random field over rectangle and derive a scaled compound Poisson field characterization for it.

Citations

• Fractional Compound Poisson Random Fields on Plane
• Point processes of the Poisson-Skellam family
• On Two Parameter Time-Changed Poisson Random Fields with Drifts
• Fox-H densities and completely monotone generalized Wright functions

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• Skellam Processes via Multiparameter Poisson Process
• Fractional Poisson Random Fields on ℝ²₊
• Fractional Compound Poisson Random Fields on Plane
• Generalized Space Time Fractional Skellam Process
• Fractional spherical random fields