Artículo
Degenerate weak convergence of row sums for arrays of random elements in stable type p Banach spaces
Autor/es | Adler, André
Ordóñez Cabrera, Manuel Hilario Rosalsky, Andrew Volodin, Andrei Igorevich |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 1999-09 |
Fecha de depósito | 2017-01-04 |
Publicado en |
|
Resumen | For an array of rowwise independent random elements {Vnj , j ≥ 1, n ≥ 1} in a real separable, stable type p Banach space X and an array of constants {anj , j ≥ 1, n ≥ 1}, general weak laws of large numbers of the forms (i) ... For an array of rowwise independent random elements {Vnj , j ≥ 1, n ≥ 1} in a real separable, stable type p Banach space X and an array of constants {anj , j ≥ 1, n ≥ 1}, general weak laws of large numbers of the forms (i) Pkn j=1 anjVnj P→ 0 and (ii) PTn j=1 anj (Vnj −cnj ) P→ 0 are obtained where for (i), EVnj = 0, j ≥ 1, n ≥ 1 and the kn are permitted to assume the value ∞ and for (ii), {cnj , j ≥ 1, n ≥ 1} is a suitable array of elements in X and {Tn, n ≥ 1} is a sequence of positive integer-valued random variables (called random indices). In the main results, the random elements {Vnj , j ≥ 1, n ≥ 1} are assumed to be stochastically dominated by a random element V and the hypotheses impose conditions on the growth behavior of the {anj , j ≥ 1, n ≥ 1}, on the tail of the distribution of ||V ||, and (for (ii)) on the marginal distributions of the random indices. The results of the form (i) are shown to be valid for a mode of convergence which is stronger than convergence in probability, viz. convergence in the Lorentz space L(p,∞)(X ). It is shown via example that the stable type p hypothesis cannot be relaxed. |
Cita | Adler, A., Ordóñez Cabrera, M.H., Rosalsky, A. y Volodin, A.I. (1999). Degenerate weak convergence of row sums for arrays of random elements in stable type p Banach spaces. Bulletin of the Institute of Mathematics. Academia Sinica, 27 (3), 187-212. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
Degenerate weak convergence of ... | 930.5Kb | [PDF] | Ver/ | |