Abstract
In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive capacity.
Highlights
As fundamental limit theorems of probability theory, the classical law of the iterated logarithm (LIL for short) plays an important role in the development of probability theory and its applications
After studying the limit theorem of sub-linear expectation, more and more research results of LIL under this framework have been obtained, the Hartman–Winter LIL were established by Chen and Hu [11] for bounded random variables, the functional central limit and Chung’s LIL were recently obtained by
The main purpose of this paper is to establish the law of iterated logarithm for linear processes generated by identically distributed (IID) random variables in sub-linear expectation space
Summary
As fundamental limit theorems of probability theory, the classical law of the iterated logarithm (LIL for short) plays an important role in the development of probability theory and its applications. A lot of literature has performed in-depth and detailed research on LIL, we can refer to Hartman and Wintner [2], Acosta [3], Shao and. Motivated by modeling uncertainty in practice, Peng [5] introduced the reasonable framework of the sub-linear expectation of random variables in a general function space. After studying the limit theorem of sub-linear expectation (e.g., see Feng [6], Deng and Wang [7], Tan and Zong [8], and Zhang [9,10], etc.), more and more research results of LIL under this framework have been obtained, the Hartman–Winter LIL were established by Chen and Hu [11] for bounded random variables, the functional central limit and Chung’s LIL were recently obtained by
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