The \( L_r \) convergence and weak laws of large numbers for \(\widetilde{\rho}\)-mixing random variables

Yanjiao Meng

Abstract


The \(L_{r}\) convergence and a class of weak laws of large numbers are obtained for sequences of \(\widetilde{\rho}\)-mixing random variables under the uniform Cesàro-type condition. This is weaker than the \(p\)th-order Cesàro uniform integrability.






doi:10.1017/S1446181117000037

Keywords


\(\widetilde{\rho}\)-mixing, uniform Cesàro-type condition, \(L_{r}\) convergence, weak law of large numbers.



DOI: http://dx.doi.org/10.21914/anziamj.v58i0.10996



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.