Local theorems for arithmetic compound renewal processes when Cramer's condition holds

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Abstract

We continue the study of the compound reneal processes (c.r.p.), where the moment Cramer's condition holds (see [1]-[10], where the study of c.r.p. was started). In the paper arithmetic c.r.p. Z(n) are studied. In such processes random vector ξ = (τ, ζ) has the arithmetic distribution, where τ > 0 defines the distance between jumps, ζ defines the values of jumps. For this processes the fine asymptotics in the local limit theorem for probabilities P(Z(n) = x) has been obtained in Cramer's deviation region of x ∈ ℤ In [6]-[10] the similar problem has benn solved for non-lattice c.r.p., when the vector ξ = (τ, ζ) has the non-lattice distribution.

Translated title of the contributionЛокальные теоремы для арифметических обобщенных процессов восстановления при выполнении условия Крамера
Original languageEnglish
Pages (from-to)21-41
Number of pages21
JournalСибирские электронные математические известия
Volume16
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • LARGE DEVIATION PRINCIPLES
  • TRAJECTORIES

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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