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Estimation of reduced Palm distributions by random methods for Cox processes with unknown probability law

Emmanuelle Crétois — 1995

Applicationes Mathematicae

Let $N_{i}$ , i ≥ 1, be i.i.d. observable Cox processes on [a,b] directed by random measures Mi. Assume that the probability law of the Mi is completely unknown. Random techniques are developed (we use data from the processes $N_{1}$ ,..., $N_{n}$ to construct a partition of [a,b] whose extremities are random) to estimate L(μ,g) = E(exp(-(N(g) - μ(g))) | N - μ ≥ 0).

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