• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.935-946
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• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• English Language & Literature Teaching
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• v.17 no.2
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• pp.79-91
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• 2011

The purpose of this paper was to take an in-depth look at early American English around the $17^{th}$ and $18^{th}$ century when immigrants from different European countries started to move into the New World. The paper attempted to describe early American English in relation to the process of immigration and settlement from a historical perspective. With a focus on major features of early American English such as uniformity, archaism and richness of lexicon, the paper tried to answer the questions such as how settlement influenced the formation and distribution of regional dialects across the continent, why immigrants tended to show a preference for a uniform way of speaking rather than choosing a variety of regional dialects for communication, and what role foreign languages played in the development of early American English. The overall findings based on the answers to these questions showed how American English went through a variety of processes and changes at the early stages of its development to become a national language later. The paper concluded with some remarks about the implications of the findings for EFL learning and the direction of future research on early American English.