Let N1tt 0 be a Poisson Process with rate Can Zt alpha N1t

Let {N1(t),t 0} be a Poisson Process with rate . Can Z(t) = alpha N1(t) + beta N2(i) ever be a Poisson Process, where alpha and beta are some non-zero constants. In other words, are there any values of alpha beta, and N2(t) such that {Z(t)t 0} is a Poisson Process. Please note that {N2(t),t 0} is not allowed to be either a Poisson Process, and is also not allowed to be a trivial random process (e.g., it is not a constant over ail time). Carefully prove or disprove.

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