On the strong law of large numbers for multivariate martingales (Q1095492)

Let \((s_ n,{\mathcal A}_ n\); \(n\geq 0)\) be a p-dimensional martingale, \(1\leq p<\infty\), with \(s_ 0=0\). Let \(B_ n\) be an \({\mathcal A}_{n-1}\)- measurable \(p\times p\)-matrix, \(n=0,1,... \). Conditions are studied under which the sequence \((B_ ns_ n)\) converges almost surely and in \(L_ q\)-metric to 0. The results are applied to multivariate linear regression.