P-asymptotically Equivalent in Probability

• Published in: Sarajevo journal of mathematics Vol. 6; no. 2; pp. 217 - 228
• Main Authors: Patterson, Richard F., Savaş, Ekrem
• Format: Journal Article
• Language: English
• Published: 11.06.2024
• ISSN: 1840-0655; 2233-1964
• DOI: 10.5644/SJM.06.2.06

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?