On the joint distribution of ladder variables of random walk |
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| Authors: | R. A. Doney P. E. Greenwood |
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| Affiliation: | (1) Department of Mathematics, University of Manchester, M13 9PL Manchester, UK;(2) Department of Mathematics, University of British Columbia, V6T 1Y4 Vancouver, B.C., Canada |
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| Abstract: | Summary The ladder timeN and ladder heightH of a random walk {Sn,n 1} as a pair (N, H) lie in the domain of attraction of a bivariate stable law ifS1 is in a domain of attraction, as was shown by Greenwood et al. (1982). In this paper we prove a converse. IfP(Sn>0) converges and (N, H) lies in a bivariate domain of attraction thenS1 is also in a domain of attraction. |
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