A note on the convergence of renewal and regenerative processes to a Brownian bridge

2007/08/27 by Foss, Sergey, Konstantopoulos, Takis
#60F17 #60G50 #60K05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0708.3667

Abstract

The standard functional central limit theorem for a renewal process with finite mean and variance, results in a Brownian motion limit. This note shows how to obtain a Brownian bridge process by a direct procedure that does not involve conditioning. Several examples are also considered.

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