Conditional limit theorems for the terms of a random walk revisited.

• Autores: Shaul K. Bar-lev, Ernst Schulte-geers, Wolfgang Stadje
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 50, Nº. 3, 2013, págs. 871-882
• Idioma: inglés
• DOI: 10.1017/s0021900200009906
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• Resumen

  • In this paper we derive limit theorems for the conditional distribution of X1 given Sn = Sn as n ? 8, where the Xi are independent and identically distributed (i.i.d.) random variables, Sn = X1 + ··· + Xn, and sn/n converges or sn = s is constant. We obtain convergence in total variation of P... to a distribution associated to that of X1 and of P... to a gamma distribution. The case of stable distributions (to which the method of associated distributions cannot be applied) is studied in detail.