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 | Enthalten in: | JOURNAL OF APPLIED PROBABILITY | Band: | 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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