Abstract
Given a counting process { ζ( t), t ≥ 0}, which is a version of a compound Poisson process and such that whenever there is a jump Δζ in the value of ζ, then Δζ = i with probability p i , i ϵ {1,…, L}. Let λ t = X be the intensity process of the associated Poisson process, where X is a random variable. Denote by B( t) the minimal σ-algebra generated by the events { ζ( t) = i}, i = 0, 1,…. The problem dealt with here is to find the estimator X e ( t) = E[ X | B( t)], t ≥ 0, of X.
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