Lecture 05: Compound and Non-Stationary Poisson Processes
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چکیده
A compound Poisson process is a real-valued point process {Zt , t ≥ 0} having the following properties. 1. finite jumps: for all ω ∈Ω, t 7−→ Zt(ω) has finitely many jumps in finite intervals. 2. independent increments: for all t,s≥ 0;Zt+s−Zt is independent of past {Zu,u≤ t}. 3. stationary increments: for all t,s≥ 0, distribution of Zt+s−Zt depends only on s and not on t. For each ω ∈Ω, we can define time and size of nth jump
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