کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1156157 | 958806 | 2015 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The uniform integrability of martingales. On a question by Alexander Cherny
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let XX be a progressively measurable, almost surely right-continuous stochastic process such that Xτ∈L1Xτ∈L1 and E[Xτ]=E[X0]E[Xτ]=E[X0] for each finite stopping time ττ. In 2006, Cherny showed that XX is then a uniformly integrable martingale provided that XX is additionally nonnegative. Cherny then posed the question whether this implication also holds even if XX is not necessarily nonnegative. We provide an example that illustrates that this implication is wrong, in general. If, however, an additional integrability assumption is made on the limit inferior of |X||X| then the implication holds. Finally, we argue that this integrability assumption holds if the stopping times are allowed to be randomized in a suitable sense.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 125, Issue 10, October 2015, Pages 3657–3662
Journal: Stochastic Processes and their Applications - Volume 125, Issue 10, October 2015, Pages 3657–3662
نویسندگان
Johannes Ruf,