Summary
We consider a point process Φ with the Polish phase space (X,X) and a system of σ-fields ℱ(x),x∈X, generated by Φ on certain sets (Γx)∈X. We define predictability for random processes indexed byX and for random measures onX and prove the existence and uniqueness of predictable and dual predictable projections under a regularity condition on Φ. ForX=ℝ +2 and under monotonicity assumptions on the sets Γx we will identify the predictable projections of some simple processes as regular versions of certain martingales.
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