A process of runs and its convergence to the brownian motion

B. G. Pittel

Stochastic Processes and their Applications, 1980, vol. 10, issue 1, 33-48

Abstract: Let X1,X2,... be i.i.d. random variables with a continuous distribution function. Let R0=0, Rk=min{j>Rk-1, such that Xj>Xj+1}, k[greater-or-equal, slanted]1. We prove that all finite-dimensional distributions of a process , converge to those of the standard Brownian motion.

Date: 1980
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