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arXiv · 0708.3667

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

Sergey Foss·Takis Konstantopoulos
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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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Sergey Foss, Takis Konstantopoulos. 2007-08-27. A note on the convergence of renewal and regenerative processes to a Brownian bridge. https://arxiv.org/abs/0708.3667

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