CONDITIONAL LIMIT THEOREMS FOR THE TERMS OF A RANDOM WALK REVISITED

Autor(en): Bar-Lev, Shaul K.
Schulte-Geers, Ernst
Stadje, Wolfgang 
Stichwörter: Conditional limit theorem; convergence in total variation; Mathematics; renewal theory; stable distribution; Statistics & Probability; sums of i.i.d. random variables
Erscheinungsdatum: 2013
Herausgeber: APPLIED PROBABILITY TRUST
Journal: JOURNAL OF APPLIED PROBABILITY
Volumen: 50
Ausgabe: 3
Startseite: 871
Seitenende: 882
Zusammenfassung: 
In this paper we derive limit theorems for the conditional distribution of X-1 given S-n = s(n) as n -> infinity, where the X-i are independent and identically distributed (i.i.d.) random variables, S-n = X-1 ... X-n, and s(n)/n converges or s(n) s is constant. We obtain convergence in total variation of P-X1 vertical bar Sn/n=s in, to a distribution associated to that of X-1 and of P-nX1 vertical bar Sn=s to a gamma distribution. The case of stable distributions (to which the method of associated distributions cannot be applied) is studied in detail.
ISSN: 00219002

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