Fractional Skellam Random Fields on $\mathbb{R}^2_+$

Abstract: We study a Skellam point process on $\mathbb{R}<sup>M_+$, $M\ge1$. For $M=2$, it reduces to a Skellam random field on plane which is a two parameter L\'evy 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.