Skellam Processes via Multiparameter Poisson Process

2025/09/16 by Vishwakarma, Pradeep · 1 citation
Engineering · #60G20 #60G55 #60G60 #FOS: Mathematics #Manufacturing Process and Optimization #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2509.12729

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

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 ℝ^M₊, M≥1 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.

Citations

• Point processes of the Poisson-Skellam family
• On a Fractional Variant of Linear Birth-Death Process
• Multiparameter Poisson Processes and Martingales

Cited by

• Time-changed generalized fractional Skellam process

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