Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales. (15th October 2015) - Wang, Caishi; Chen, Jinshu
Abstract : The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingaleM . A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strongly convergent. A type of generalized martingales associated withM is introduced and their convergence theorems are established. Some applications are also shown.