Given a Poisson process $\left\{N_t\right\}_{t\ge \ 0}$, we need to find the following $P\left\{\cap \ _{r=0}^mN_r=2r\right\}$. But the aforementioned notation doesn't make any sense at all. What is the meaning of the intersection operator in this context? Please note I am not asking for the the answer to the expression itself and please note that I am aware of all the tools used in solving probabilities expectations related to Poisson processes taught in a typical introductory Stochastic processes class.
2026-03-30 08:59:33.1774861173
Meaning of intersection of Poisson processes
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