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This is a Quantitative Study study.

October 13, 2025Open Access

Fractional Skellam Random Fields on R²_+

Key Points

A weak convergence result for the Skellam random field on the plane is established.
Three fractional variants of the Skellam random field are analyzed for point probabilities and governing equations.
An integral of the Skellam random field over a rectangle leads to a characterization by a compound Poisson field.
The study details various distributional properties of the Skellam point process on the positive quadrant of the plane.

Abstract

We study a Skellam point process on RM_+, M1. 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.

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Cite This Study

Pradeep Vishwakarma (Sat,) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec09292 https://doi.org/https://doi.org/10.48550/arxiv.2509.10870

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