Combinatorial stochastic processes (Q1336987)

Well-known asymptotic results for sums of independent stochastic processes are extended to processes \(S = \sum^ n_{i = 1} \varphi_{i \pi (i)}\), where \(\varphi = (\varphi_{ij})_{1 \leq i,j \leq n}\) is a collection of independent stochastic processes \(\varphi_{ij}\) on some set \(\tau\), and \(\pi\) is a random permutation of \(\{1,2, \dots, n\}\) such that \(\pi\), \(\varphi\) are independent. The general results, a uniform law of large numbers and a functional central limit theorem, are applied to permutation processes and randomized trials. Classical applications are rank tests and permutation tests.