TY - JOUR

T1 - Local theorems for arithmetic compound renewal processes when Cramer's condition holds

AU - Mogulskii, Anatolii Alfredovich

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - LARGE DEVIATION PRINCIPLES

KW - TRAJECTORIES

UR - http://www.scopus.com/inward/record.url?scp=85071198002&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=42735047

U2 - 10.33048/semi.2019.16.002

DO - 10.33048/semi.2019.16.002

M3 - Article

AN - SCOPUS:85071198002

VL - 16

SP - 21

EP - 41

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -