ترغب بنشر مسار تعليمي؟ اضغط هنا

Equivalent conditions of complete convergence for weighted sums of sequences of i. i. d. random variables under sublinear expectations

86   0   0.0 ( 0 )
 نشر من قبل Mingzhou Xu
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

The complete convergence for weighted sums of sequences of independent, identically distributed random variables under sublinear expectations space was studied. By moment inequality and truncation methods, we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent, identically distributed random variables under sublinear expectations space. The results extend the corresponding results obtained by Guo (2012) to those for sequences of independent, identically distributed random variables under sublinear expectations space.



قيم البحث

اقرأ أيضاً

98 - Mingzhou Xu , Kun Cheng 2021
In this paper, we prove the equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent, identically distributed random variables under sublinear expectations space. As applications, the Baum-Katz type results for the maximum for partial weighted sums of independent, identically distributed random variables are established under sublinear expectations space. The results obtained in the article are the extensions of the equivalent conditions of complete moment convergence of the maximum under classical linear expectation space.
Under the sublinear expectation $mathbb{E}[cdot]:=sup_{thetain Theta} E_theta[cdot]$ for a given set of linear expectations ${E_theta: thetain Theta}$, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the $G$-normal distribution, which was used as the limit in Peng (2007)s central limit theorem, in a probability space.
This short note provides a new and simple proof of the convergence rate for Pengs law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
212 - Shige Peng 2008
We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertai nty can be also described. W present our new result of central limit theorem under sublinear expectation. This theorem can be also regarded as a generalization of the law of large number in the case of mean-uncertainty.
78 - Shui Feng 2021
Let ${{bf mathcal{Z}}_n:ngeq 1}$ be a sequence of i.i.d. random probability measures. Independently, for each $ngeq 1$, let $(X_{n1},ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper studies the large devi ation principles for the randomly weighted sum $sum_{i=1}^{n} X_{ni} mathcal{Z}_i$. In the case of finite Dirichlet weighted sum of Dirac measures, we obtain an explicit form for the rate function. It provides a new measurement of divergence between probabilities. As applications, we obtain the large deviation principles for a class of randomly weighted means including the Dirichlet mean and the corresponding posterior mean. We also identify the minima of relative entropy with mean constraint in both forward and reverse directions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا