Strong laws of large numbers for arrays of row-wise exchangeable random elements (Q1062335)

Let \(\{X_{n,k}:\) \(1\leq k\leq n\), \(n\geq 1\}\) be a triangular array of row-wise exchangeable random variables with values in a separable Banach space. The authors study the almost sure convergence to 0 of \(n^{- 1/p}\sum^{n}_{k=1}X_{n,k}\), \(1\leq p<2\), using martingale methods under varying moment and distribution conditions on the random variables. They obtain in particular strong laws of large numbers in Banach spaces of stable type p and prove consistency of the kernel density estimates in this setting.