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
JournalSiberian Electronic Mathematical Reports
Publication statusPublished - 1 Nov 2019


  • Compound multidimensional renewal process
  • Cramer's condition
  • Deviation (rate) function
  • Fundamental function
  • Large deviations
  • Renewal measure
  • Second deviation (rate) function

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