Seminario del dott. Giovanni Luca Torrisi (CNR-Istituto per le Applicazioni del Calcolo).
Abstract:
We give a quantitative Gaussian and Poisson approximation for the first chaos (or innovation) of spatial point processes with conditional intensity. To this aim we use a Malliavin-Stein-Chen approach. This method is essentially based on the following two steps. First, we provide an integration by parts (IBP) formula which relates the first chaos with the discrete Malliavin operator. Second, we derive the probability approximations by combining the IBP formula with the Stein and Chen methods. Our findings extend the corresponding results on the Poisson space due to Peccati, Solè, Taqqu and Utzet (2010) and Peccati (2011). The general bounds presented in this talk are applied to stationary, inhibitory and finite range Gibbs point processes with pair potential, providing explicit error bounds and quantitative limit theorems.