On complete convergence of the sum of a random number of a stable type P random elements
Complete convergence for randomly indexed normalized sums of random elements of the form ∑j=1TnXj/ϕ(Tn) is established. The random elements {Xn} belong to a type p stable space and are assumed to be independent, but not necessarily identically distributed. No assumptions are placed on the joint dist...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000032 |
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| _version_ | 1832559864285495296 |
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| author | André Adler Andrey Volodin |
| author_facet | André Adler Andrey Volodin |
| author_sort | André Adler |
| collection | DOAJ |
| description | Complete convergence for randomly indexed normalized sums of random
elements of the form ∑j=1TnXj/ϕ(Tn) is established. The random elements {Xn} belong to
a type p stable space and are assumed to be independent, but not necessarily identically
distributed. No assumptions are placed on the joint distributions of the stopping times
{Tn}. |
| format | Article |
| id | doaj-art-d38b44cfe4e24e47b36f02a02837d6e8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d38b44cfe4e24e47b36f02a02837d6e82025-02-03T01:29:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-01181333610.1155/S0161171295000032On complete convergence of the sum of a random number of a stable type P random elementsAndré Adler0Andrey Volodin1Department of Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USAResearch Institute of Mathematics, Kazan University, Tatarstan, Kazan 420008, RussiaComplete convergence for randomly indexed normalized sums of random elements of the form ∑j=1TnXj/ϕ(Tn) is established. The random elements {Xn} belong to a type p stable space and are assumed to be independent, but not necessarily identically distributed. No assumptions are placed on the joint distributions of the stopping times {Tn}.http://dx.doi.org/10.1155/S0161171295000032complete convergencestable type p. |
| spellingShingle | André Adler Andrey Volodin On complete convergence of the sum of a random number of a stable type P random elements International Journal of Mathematics and Mathematical Sciences complete convergence stable type p. |
| title | On complete convergence of the sum of a random number of a stable type P random elements |
| title_full | On complete convergence of the sum of a random number of a stable type P random elements |
| title_fullStr | On complete convergence of the sum of a random number of a stable type P random elements |
| title_full_unstemmed | On complete convergence of the sum of a random number of a stable type P random elements |
| title_short | On complete convergence of the sum of a random number of a stable type P random elements |
| title_sort | on complete convergence of the sum of a random number of a stable type p random elements |
| topic | complete convergence stable type p. |
| url | http://dx.doi.org/10.1155/S0161171295000032 |
| work_keys_str_mv | AT andreadler oncompleteconvergenceofthesumofarandomnumberofastabletypeprandomelements AT andreyvolodin oncompleteconvergenceofthesumofarandomnumberofastabletypeprandomelements |