Accession Number : AD0665659

Title :   CONVERGENCE IN DISTRIBUTION OF STOCHASTIC INTEGRALS.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Brown,Mark

Report Date : 30 JAN 1968

Pagination or Media Count : 55

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.

Descriptors :   (*DISTRIBUTION THEORY, *STOCHASTIC PROCESSES), RADIOACTIVE DECAY, HILBERT SPACE, OPERATORS(MATHEMATICS), MAPPING(TRANSFORMATIONS), STATISTICAL PROCESSES, MEASURE THEORY, SET THEORY, INTEGRALS, RANDOM VARIABLES, CONVERGENCE, RELIABILITY, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE