Lecture-30: Compound and Non-Stationary Poisson Processes
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چکیده
Let (Nt : t > 0) be the simple counting process associated with the number of jumps in (0, t]. Then, Sn and Xn are the respectively the arrival instant and the size of the nth jump, and we can write Zt = ∑t i=1 Xi. Let Fs = σ(Zu : u ∈ (0,s]), and F• = (Fs : s> 0) be the natural filtration associated with the process Z. Clearly, jump times (Sn : n∈N) are stopping times with respect to filtration F•.
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