Assume $X_1(t)$, $X_2(t)$ are two poisson processes with parameters $\rho_1$, $\rho_2$ accordingly. Suppose $Z(t)=X_1(t)=X_1(t)-X_2(t)$. At first I'm interest in knowing generators of the process $Z(t)$ . Now if $\rho_1>\rho_2$, define $T=\inf\{t:Z(t)=1\}$ . What will be $E(t)$? And at the end I need $Var(T)$. Thank you for your helps.
2026-04-03 21:30:28.1775251828
Generators of difference of two poisson processes
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