P-asymptotically Equivalent in Probability
In this paper we present the following definitions P-asymptotically equivalent probability of multiple $L$ and P-asymptotically probability regular. In addition to these definitions we asked and provide answers for the following questions. (1)If $x\stackrel{Probability}{\approx} y$ then what type of...
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| Published in | Sarajevo journal of mathematics Vol. 6; no. 2; pp. 217 - 228 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
11.06.2024
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| Online Access | Get full text |
| ISSN | 1840-0655 2233-1964 |
| DOI | 10.5644/SJM.06.2.06 |
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| Summary: | In this paper we present the following definitions P-asymptotically equivalent probability of multiple $L$ and P-asymptotically probability regular. In addition to these definitions we asked and provide answers for the following questions.
(1)If $x\stackrel{Probability}{\approx} y$ then what type of four dimensional matrices transformation will satisfy the following $\mu (Ax)\stackrel{Probability}{\approx} \mu (Ay)$?
(2) If $[x]$ and $[y]$ are bounded double sequences that P-asymptotically converges at the same rate, then what are the necessary and sufficient conditions on the entries of any four dimensional matrix transformation $A$ that will ensure that $A$ sums $[x]$ and $[y]$ at the same P-asymptotic rate?
(3) What are the conditions on the entries of four dimensional matrices that ensure the preservation of P-asymptotically convergence in probability? |
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| ISSN: | 1840-0655 2233-1964 |
| DOI: | 10.5644/SJM.06.2.06 |