کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10527335 958825 2010 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Laws relating runs and steps in gambler's ruin
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Laws relating runs and steps in gambler's ruin
چکیده انگلیسی
Let Xj denote a fair gambler's ruin process on Z∩[−N,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 N→∞, N−2RN converges in distribution to a density with Laplace transform: tanh(λ)/λ. In law, we find: 2(limN→∞N−2RN)=limN→∞N−2LN. Denote by RN′ and LN′ the number of runs and steps respectively in the meander portion of the gambler's ruin process. Then, N−1(2RN′−LN′) converges in law as N→∞ to the density (π/4)sech2(πx/2),−∞
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 125, Issue 5, May 2015, Pages 2010-2025
نویسندگان
,