Abstract
The aim of this paper is to study and establish the precise asymptotics for complete integral convergence theorems under a sublinear expectation space. As applications, the precise asymptotics for p0≤p≤2 order complete integral convergence theorems have been generalized to the sublinear expectation space context. We extend some precise asymptotics for complete moment convergence theorems from the traditional probability space to the sublinear expectation space. Our results generalize corresponding results obtained by Liu and Lin (2006). There is no report on the precise asymptotics under sublinear expectation, and we provide the method to study this subject.
Highlights
Because the sublinear expectation provides a very flexible framework to model sublinear probability problems, the limit theorems of the sublinear expectation have received more and more attention and research recently
Peng [1, 7, 8] constructed the basic framework, basic properties, and central limit theorem under sublinear expectations, Zhang [9,10,11] established the exponential inequalities, Rosenthal’s inequalities, strong law of large numbers, and law of iterated logarithm, Hu [12], Chen [13], and Wu and Jiang [14] studied strong law of large numbers, Wu et al [15] studied the asymptotic approximation of inverse moment, Xi et al [16] and Lin and Feng [17] studied complete convergence, and so on
In sublinear expectations, due to the uncertainty of expectation and capacity, the precise asymptotics is essentially different from the ordinary probability space
Summary
E aim of this paper is to study and establish the precise asymptotics for complete integral convergence theorems under a sublinear expectation space. The precise asymptotics for p (0 ≤ p ≤ 2) order complete integral convergence theorems have been generalized to the sublinear expectation space context. E purpose of this paper is to establish the precise asymptotics theorems for p (0 ≤ p ≤ 2) order complete integral convergence for independent and identically distributed random variables under sublinear expectation. X>1 e combination of (41) and (32) is established. is completes the proof of Lemma 5
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
