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September 2013 Conditional limit theorems for the terms of a random walk revisited
Shaul K. Bar-Lev, Ernst Schulte-Geers, Wolfgang Stadje
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J. Appl. Probab. 50(3): 871-882 (September 2013). DOI: 10.1239/jap/1378401242

Abstract

In this paper we derive limit theorems for the conditional distribution of X1 given Sn=sn as n→ ∞, where the Xi are independent and identically distributed (i.i.d.) random variables, Sn=X1+··· +Xn, and sn/n converges or sns is constant. We obtain convergence in total variation of PX1Sn/n=s to a distribution associated to that of X1 and of PnX1Sn=s to a gamma distribution. The case of stable distributions (to which the method of associated distributions cannot be applied) is studied in detail.

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Shaul K. Bar-Lev. Ernst Schulte-Geers. Wolfgang Stadje. "Conditional limit theorems for the terms of a random walk revisited." J. Appl. Probab. 50 (3) 871 - 882, September 2013. https://doi.org/10.1239/jap/1378401242

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1284.60049
MathSciNet: MR3102520
Digital Object Identifier: 10.1239/jap/1378401242

Subjects:
Primary: 60F05
Secondary: 60K05

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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