Flint, Ian et Torrisi, Giovanni Luca, A Clark.Ocone formula for temporal point processes and applications, Annals of probability (Online) , 45(5), 2017, pp. 3266-3292
We provide a Clark.Ocone formula for square-integrable functionals of a general temporal point process satisfying only a mild moment condition, generalizing known results on the Poisson space. Some classical applications are given, namely a deviation bound and the construction of a hedging portfolio in a pure-jump market model. As a more modern application, we provide a bound on the total variation distance between two temporal point processes, improving in some sense a recent result in this direction.