Can we define a 2-D Poisson process such that one of the dimensions is spatial and other in time? Or in other words, if I define a process in space and time such that in any disjoint interval of space and time, the number of occurrences are independent and Poisson distributed with some rate $\lambda$ whose dimension is $1/(space.time)$. Then will the resulting process be a Poisson process? Is there any good literature available where this kind of applications are found?
2026-04-01 10:50:12.1775040612
Poisson process in 2-D
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