Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527335 | Stochastic Processes and their Applications | 2010 | 16 Pages |
Abstract
Let Xj denote a fair gambler's ruin process on Zâ©[âN,N] started from X0=0, and denote by RN the number of runs of the absolute value, |Xj|, until the last visit j=LN by Xj to 0. Then, as Nââ, Nâ2RN converges in distribution to a density with Laplace transform: tanh(λ)/λ. In law, we find: 2(limNââNâ2RN)=limNââNâ2LN. Denote by RNâ² and LNâ² the number of runs and steps respectively in the meander portion of the gambler's ruin process. Then, Nâ1(2RNâ²âLNâ²) converges in law as Nââ to the density (Ï/4)sech2(Ïx/2),ââ
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Gregory J. Morrow,