Abstract
If a planar point process N is adapted to a filtration endowed with the property of conditional independence [denoted by (F4)], a compensator A* may be defined such that N — A* is a strong martingale. It is shown that, under certain conditions, there exists a discrete strong LA-approximation for A*. This approximation is used to find an upper bound for the total variation distance between N(s, t) and a Poisson random variable in terms of A*. If (F4) is not satisfied, a bound may be expressed in terms of two one-dimensional compensators. Examples are given, and it is shown that the A* bound may improve on bounds available through existing one-dimensional techniques.
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