Large deviation principle for multidimensional first compound renewal processes in the phase space

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3 Citations (Scopus)

Abstract

We obtain the large deviation principles for multidimensional first compound renewal processes Z(t) in the phase space Rd, for this we find and investigate the rate function DZ(α). Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function AZ(μ).

Original languageEnglish
Article number101
Pages (from-to)1464-1477
Number of pages14
JournalСибирские электронные математические известия
Volume16
DOIs
Publication statusPublished - 1 Nov 2019

Keywords

  • Compound multidimensional renewal process
  • Cramer's condition
  • Deviation (rate) function
  • Fundamental function
  • Large deviations
  • Renewal measure
  • Second deviation (rate) function
  • large deviations
  • INTEGRO-LOCAL THEOREMS
  • compound multidimensional renewal process
  • fundamental function
  • second deviation (rate) function
  • renewal measure
  • deviation (rate) function

OECD FOS+WOS

  • 1.01 MATHEMATICS

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