کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1156008 958793 2010 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Ergodic theorems for extended real-valued random variables
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Ergodic theorems for extended real-valued random variables
چکیده انگلیسی

We first establish a general version of the Birkhoff Ergodic Theorem for quasi-integrable extended real-valued random variables without assuming ergodicity. The key argument involves the Poincaré Recurrence Theorem. Our extension of the Birkhoff Ergodic Theorem is also shown to hold for asymptotic mean stationary sequences. This is formulated in terms of necessary and sufficient conditions. In particular, we examine the case where the probability space is endowed with a metric and we discuss the validity of the Birkhoff Ergodic Theorem for continuous random variables. The interest of our results is illustrated by an application to the convergence of statistical transforms, such as the moment generating function or the characteristic function, to their theoretical counterparts.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 120, Issue 10, September 2010, Pages 1908–1919
نویسندگان
, , ,