Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. I

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7 Citations (Scopus)

Abstract

In the work, which consists of 4 papers (the article and [15]-[17]), we obtain integro-local limit theorems in the phase space for multidimensional compound renewal processes, when Cramer's condition holds. In the part I (the article) we consider the so-called first renewal process Z(t) in a regular region, which is an of analog Cramer's deviation region for random walk. The regular region includes normal and moderate deviations.

Translated title of the contributionИнтегро-локальные теоремы для многомерных обобщенных процессов восстановления при моментном условии Крамера. I
Original languageEnglish
Pages (from-to)475-502
Number of pages28
JournalСибирские электронные математические известия
Volume15
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • compound multidimensional renewal process
  • first (second) renewal process
  • large deviations
  • integro-local limit theorems
  • renewal measure
  • Cramer's condition
  • deviation (rate) function
  • second deviation (rate) function

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27.43 Probability Theory and mathematical statistics

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