Let's say we have quanta for the rate, $\lambda$, of some specific event occuring in $1 cm^3$ volume per second so that $\lambda$'s unit is $\frac{1}{cm^3-s}$. This occuring of events can be represented as Poisson distribution. Is it mathematically possible to find the rate of this event occuring on a surface such that new $\lambda^*$ has $\frac{1}{cm^2-s}$ unit?
2026-03-27 18:35:40.1774636540
Is it possible to map 3D Poisson process to 2D poisson process?
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If I understand the question correctly:
The rate of events occurring in each surface is zero (there is a continuum of surfaces and if they had positive rate the total rate would be infinite).
Think of the regular one-dimensional Poisson process such that $N(t)\sim$Poisson$(\lambda t)$. What is the rate at any given point $t\in\mathbb{R}$?