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On Two Parameter Time-Changed Poisson Random Fields with Drifts

Probability 2025-03-07 v1

Abstract

We study the composition of bivariate L\'evy process with bivariate inverse subordinator. The explicit expressions for its dispersion and auto correlation matrices are obtained. Also, the time-changed two parameter L\'evy processes with rectangular increments are studied. We introduce some time-changed variants of the Poisson random field in plane with and without drift, and derive the associated fractional differential equations for their distributions. Later, we consider some time-changed L\'evy processes where the time-changing components are two parameter Poisson random fields with drifts. Moreover, two parameter coordinatewise semigroup operators associated with some of the introduced processes are discussed.

Keywords

Cite

@article{arxiv.2503.04166,
  title  = {On Two Parameter Time-Changed Poisson Random Fields with Drifts},
  author = {Pradeep Vishwakarma and Manisha Dhillon and Kuldeep Kumar Kataria},
  journal= {arXiv preprint arXiv:2503.04166},
  year   = {2025}
}
R2 v1 2026-06-28T22:08:48.176Z