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

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.

Convergence for sums of i. i. d. random variables under sublinear expectations

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.

Document Graph for Neural Machine Translation

Previous works have shown that contextual information can improve the performance of neural machine translation (NMT). However, most existing document-level NMT methods only consider a few number of previous sentences. How to make use of the whole document as global contexts is still a challenge. To address this issue, we hypothesize that a document can be represented as a graph that connects relevant contexts regardless of their distances. We employ several types of relations, including adjacency, syntactic dependency, lexical consistency, and coreference, to construct the document graph. Then, we incorporate both source and target graphs into the conventional Transformer architecture with graph convolutional networks. Experiments on various NMT benchmarks, including IWSLT English--French, Chinese-English, WMT English--German and Opensubtitle English--Russian, demonstrate that using document graphs can significantly improve the translation quality. Extensive analysis verifies that the document graph is beneficial for capturing discourse phenomena.

Moderate deviations for empirical measures for nonhomogeneous Markov chains

We prove that moderate deviations for empirical measures for countable nonhomogeneous Markov chains hold under the assumption of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chains in Ces`aro sense.

Central Limit Theorem and Moderate deviation for nonhomogenenous Markov chains

Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces`aro sense. Furthermore, we obtain a corresponding moderate deviation theorem for countable nonhomogeneous Markov chain by Gartner-Ellis theorem and exponential equivalent method.