We continue the study of the compound reneal processes(c.r.p.), where the moment Cramer’s condition holds (see [1]—[10], wherethe study of c.r.p. was started). In the paper arithmetic c.r.p. Z(n) arestudied. In such processes random vector = ( ; ) has the arithmeticdistribution, where 0 defines the distance between jumps, definesthe values of jumps. For this processes the fine asymptotics in the locallimit theorem for probabilities P(Z(n) = x) has been obtained in Cramer’sdeviation region of x 2 Z In [6]—[10] the similar problem has benn solvedfor non-lattice c.r.p., when the vector = ( ; ) has the non-latticedistribution.
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