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A q-Generalization of Product Densities and Janossy Functions in Stochastic Point Processes

R. Parthasarathy·R. Sridhar
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Abstract

A q-generalization of the product densities in stochastic point processes is developed. The properties of these functions are studied and a q-generalization of the usual $C^r_s$ coefficients is obtained. This for fixed q-number of particles coincides with the q-Stirling numbers of the second kind. The q-product densities are investigated using q-Poisson distribution and this shows that the stochastic point processes involving consistent q-generalization are inherently correlated. A closely related function to q-product densities is a q-generalized Janossy function and a relation between the two is established.

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R. Parthasarathy, R. Sridhar. 2004-03-30. A q-Generalization of Product Densities and Janossy Functions in Stochastic Point Processes. https://arxiv.org/abs/math-ph/0403059

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