Skellam Processes via Multiparameter Poisson Process

Pradeep Vishwakarma

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arXiv · 2509.12729

Skellam Processes via Multiparameter Poisson Process

Pradeep Vishwakarma

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Abstract

We introduce a mltiparameter version of Skellam point process via multiparameter Poisson processes. Its distributional properties are studied in detail. Its compound representation is derived for a particular case. Also, its Riemann integral over a rectangle in $\mathbb{R}^M_+$, $M\ge1$ is introduced and a closed expression for its characteristic function is obtained. Later, we introduce a different version of multiparameter Skellam process, and derive a weak convergence result for it. Moreover, a two parameter fractional Skellam process is discussed.

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Pradeep Vishwakarma. 2025-09-16. Skellam Processes via Multiparameter Poisson Process. https://arxiv.org/abs/2509.12729

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