2021/07/08 by Antonella Calzolari, Calzolari, Antonella, Barbara Torti +1
Mathematics · #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2107.04087
openalex publication_date 2021/07/08 · openalex created_date 2022/07/25 · openalex updated_date 2026/08/01
We show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove that a strong representation holds if any multivariate point process of the vector has almost surely infinite explosion time and discrete mark's space. Then we provide a condition under which the components of the multidimensional local martingale driving the strong representation are pairwise orthogonal.