A functional limit convergence towards brownian excursion

2010/12/01 by Julien Sohier, Sohier, Julien · 1 citation
Economics, Econometrics and Finance · Mathematics · #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1012.0118

arxiv created 2010/12/01 · arxiv updated 2010/12/02

Abstract

We consider a random walk S in the domain of attraction of a standard normal law Z, ie there exists a positive sequence a_n such that S_n/a_n converges in law towards Z. The main result of this note is that the rescaled process (S_{\lfloor nt \rfloor}/a_n, t ≥ 0) conditioned to stay non-negative, to start and to come back near the origin converges in law towards the normalized brownian excursion.

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