Precise Asymptotics for Complete Integral Convergence under Sublinear Expectations
Qunying Wu
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>p</mml:mi></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>p</mml:mi><mml:mo>≤</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfenced></mml:mrow></mml:math> 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.