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arxiv: 0708.3667 · v1 · pith:CUFHAMTNnew · submitted 2007-08-27 · 🧮 math.PR

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

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keywords brownianbridgelimitnoteprocessrenewalcentralconditioning
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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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