Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales

Caishi Wang; Jinshu Chen

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arXiv · 1510.04639

Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales

Caishi Wang·Jinshu Chen

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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 martingale $M$. A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strong convergent. A type of generalized martingales associated with $M$ are introduced and their convergence theorems are established. Some applications are also shown.

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Caishi Wang, Jinshu Chen. 2015-10-15. Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales. https://arxiv.org/abs/1510.04639

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