کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10527189 958732 2014 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Non-homogeneous random walks on a semi-infinite strip
ترجمه فارسی عنوان
راه رفتن تصادفی غیر همگن بر روی نوار نیمه بی نهایت است
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی
We study the asymptotic behaviour of Markov chains (Xn,ηn) on Z+×S, where Z+ is the non-negative integers and S is a finite set. Neither coordinate is assumed to be Markov. We assume a moments bound on the jumps of Xn, and that, roughly speaking, ηn is close to being Markov when Xn is large. This departure from much of the literature, which assumes that ηn is itself a Markov chain, enables us to probe precisely the recurrence phase transitions by assuming asymptotically zero drift for Xn given ηn. We give a recurrence classification in terms of increment moment parameters for Xn and the stationary distribution for the large- X limit of ηn. In the null case we also provide a weak convergence result, which demonstrates a form of asymptotic independence between Xn (rescaled) and ηn. Our results can be seen as generalizations of Lamperti's results for non-homogeneous random walks on Z+ (the case where S is a singleton). Motivation arises from modulated queues or processes with hidden variables where ηn tracks an internal state of the system.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 124, Issue 10, October 2014, Pages 3179-3205
نویسندگان
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