Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/360679 |
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| _version_ | 1832561416250327040 |
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| author | Caishi Wang Jinshu Chen |
| author_facet | Caishi Wang Jinshu Chen |
| author_sort | Caishi Wang |
| collection | DOAJ |
| description | 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 strongly convergent. A type of generalized martingales associated with M is introduced and their convergence theorems are established.
Some applications are also shown. |
| format | Article |
| id | doaj-art-35aaf3b979b14182b2dbff92c367cbf0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-35aaf3b979b14182b2dbff92c367cbf02025-02-03T01:25:06ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/360679360679Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal MartingalesCaishi Wang0Jinshu Chen1School of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaSchool of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, ChinaThe 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 strongly convergent. A type of generalized martingales associated with M is introduced and their convergence theorems are established. Some applications are also shown.http://dx.doi.org/10.1155/2015/360679 |
| spellingShingle | Caishi Wang Jinshu Chen Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales Journal of Function Spaces |
| title | Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales |
| title_full | Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales |
| title_fullStr | Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales |
| title_full_unstemmed | Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales |
| title_short | Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales |
| title_sort | convergence theorems for generalized functional sequences of discrete time normal martingales |
| url | http://dx.doi.org/10.1155/2015/360679 |
| work_keys_str_mv | AT caishiwang convergencetheoremsforgeneralizedfunctionalsequencesofdiscretetimenormalmartingales AT jinshuchen convergencetheoremsforgeneralizedfunctionalsequencesofdiscretetimenormalmartingales |