The Clark-Ocone formula and the Poincare' inequality for point processes

Clark-Ocone formulas are powerful results in stochastic analysis with a variety of applications. In the talk we provide the Clark-Ocone formula for square-integrable functionals of point processes with stochastic intensity. Then we present two applications of the formula: the Poincare' inequality and a concentration bound for those functionals. Our results generalize the corresponding ones on the Poisson space. The talk is based on joint works with Ian Flint and Nicolas Privault (NTU, Singapore)