Distribution-valued iterated gradient and chaotic decompositions of Poisson jump times functionals (Q699463)

The main result of this paper is chaotic expansion of the random variable \(f(T_1,\ldots, T_n)\), where \(f\) is a smooth bounded function and \(T_1, \ldots, T_n\) are the jumping times of the standard Poisson process. It gives another look at a previous result of the author himself [Stat. Probab. Lett. 43, No. 2, 179-188 (1999; Zbl 0938.60077)] which hinged upon the Charlier polynomials. The main tool is an iteration procedure on a modification of the classical Carlen-Pardoux differential operator on Poisson space.