On Two Parameter Time-Changed Poisson Random Fields with Drifts

Pradeep Vishwakarma; Manisha Dhillon; Kuldeep Kumar Kataria

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arXiv · 2503.04166

On Two Parameter Time-Changed Poisson Random Fields with Drifts

Pradeep Vishwakarma·Manisha Dhillon·Kuldeep Kumar Kataria

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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.

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Pradeep Vishwakarma, Manisha Dhillon, Kuldeep Kumar Kataria. 2025-03-06. On Two Parameter Time-Changed Poisson Random Fields with Drifts. https://arxiv.org/abs/2503.04166

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