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 contribution | Локальные теоремы для арифметических обобщенных процессов восстановления при выполнении условия Крамера |
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Original language | English |
Pages (from-to) | 21-41 |
Number of pages | 21 |
Journal | Сибирские электронные математические известия |
Volume | 16 |
DOIs | |
Publication status | Published - 1 Jan 2019 |
Keywords
- LARGE DEVIATION PRINCIPLES
- TRAJECTORIES
OECD FOS+WOS
- 1.01 MATHEMATICS
State classification of scientific and technological information
- 27 MATHEMATICS