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

Shaul K. Bar-lev, Ernst Schulte-geers, Wolfgang Stadje

• 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.