I would like to ask about some literature depending compound process. I want to find some limit theorem for process: $$Z(t)=\sum_{i=1}^{N_{1}(t)}X_{i}-\sum_{j=1}^{N_{2}(t)}Y_{j}, $$ where $N_{1}, N_{2}$ are two Poisson processes with intensity $\lambda_{1}$, $\lambda_{2}$ and they are somehow dependent. I don't know how to start and where can I find something about this topic. Because variables $X_{i}$ and $Y_{j}$ have different distributies I can not transform it into one sum. Do you know some good literature helpiing with this problem?
2026-03-25 06:26:38.1774419998
Sum of compound Poisson processes with dependent counting process
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