Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales
2015
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 martingale . 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 with is introduced and their convergence theorems are established.
Some applications are also shown.
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