Mean convergence theorem for multidimensional arrays of random elements in Banach spaces.
Mesures aléatoires localement finies
Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation
In [A. Genadot and M. Thieullen, Averaging for a fully coupled piecewise-deterministic markov process in infinite dimensions. Adv. Appl. Probab. 44 (2012) 749–773], the authors addressed the question of averaging for a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimensions. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuations of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated...