Strong Laws of Large Numbers for 𝔹-Valued Random Fields
We extend to random fields case, the results of Woyczynski, who proved Brunk's type strong law of large numbers (SLLNs) for 𝔹-valued random vectors under geometric assumptions. Also, we give probabilistic requirements for above-mentioned SLLN, related to results obtained by Acosta as well as n...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/485412 |
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| author | Zbigniew A. Lagodowski |
| author_facet | Zbigniew A. Lagodowski |
| author_sort | Zbigniew A. Lagodowski |
| collection | DOAJ |
| description | We extend to random fields case, the results of Woyczynski, who proved
Brunk's type strong law of large numbers (SLLNs) for 𝔹-valued random vectors under geometric
assumptions. Also, we give probabilistic requirements for above-mentioned
SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic
conditions for the geometry of Banach space associated to the strong and
weak law of large numbers for multidimensionally indexed random vectors. |
| format | Article |
| id | doaj-art-6a0fad5df7ca4452af353f33f99ac833 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6a0fad5df7ca4452af353f33f99ac8332025-02-03T01:22:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/485412485412Strong Laws of Large Numbers for 𝔹-Valued Random FieldsZbigniew A. Lagodowski0Department of Mathematics, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, Nadbystrzycka Street 38A, 20-618 Lublin, PolandWe extend to random fields case, the results of Woyczynski, who proved Brunk's type strong law of large numbers (SLLNs) for 𝔹-valued random vectors under geometric assumptions. Also, we give probabilistic requirements for above-mentioned SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic conditions for the geometry of Banach space associated to the strong and weak law of large numbers for multidimensionally indexed random vectors.http://dx.doi.org/10.1155/2009/485412 |
| spellingShingle | Zbigniew A. Lagodowski Strong Laws of Large Numbers for 𝔹-Valued Random Fields Discrete Dynamics in Nature and Society |
| title | Strong Laws of Large Numbers for 𝔹-Valued Random Fields |
| title_full | Strong Laws of Large Numbers for 𝔹-Valued Random Fields |
| title_fullStr | Strong Laws of Large Numbers for 𝔹-Valued Random Fields |
| title_full_unstemmed | Strong Laws of Large Numbers for 𝔹-Valued Random Fields |
| title_short | Strong Laws of Large Numbers for 𝔹-Valued Random Fields |
| title_sort | strong laws of large numbers for 𝔹 valued random fields |
| url | http://dx.doi.org/10.1155/2009/485412 |
| work_keys_str_mv | AT zbigniewalagodowski stronglawsoflargenumbersforbvaluedrandomfields |