Abstract
Abstract : A type of convergence of stochastic processes, convergence in linear law, is introduced. It entails convergence of finite dimensional distributions and a condition on the covariance kernels of the processes. A method is presented under which a sequence of finite collections of random variables, with suitable covariance structure, may be embedded in a sequence of continuous time processes satisfying the covariance conditions for linear law convergence. The paper illustrates that certain functionals of stochastic processes can be shown to converge in distribution to the corresponding functional of the limiting process, without an analysis of sample paths. Applications to limiting distributions of linear combinations of order statistics and linear combinations of successive differences of order statistics are presented. Limiting distributions are also obtained for certain random variables arising in nuclear chemistry and reliability.
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