Geodesic
Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds.~III
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 528-553.

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In the work, which consists of 4 papers (the article and [3]–[5]), we obtain integro-local limit theorems in the phase space for multidimensional compound renewal processes, when Cramer's condition holds. In the part III (the article) we consider the so-called second renewal process in a regular deviation region.
Keywords: compound multidimensional renewal process, second renewal process, large deviations, integro-local limit theorems, renewal measure, Cramer's condition, deviation (rate) function, second deviation (rate) function. 
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     author = {A. A. Mogulskii and E. I. Prokopenko},
     title = {Integro-local theorems for multidimensional compound renewal processes, when {Cramer's} condition {holds.~III}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {528--553},
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A. A. Mogulskii; E. I. Prokopenko. Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds.~III. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 528-553. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a37/

[1] A.A. Borovkov, A.A. Mogulskii, “Integro-local limit theorems for compound renewal processes with Cramer's condition I”, Siberian Mathematical Journal, 59:3 (2018), 491–514

[2] A.A. Borovkov, A.A. Mogulskii, “Integro-local limit theorems for compound renewal processes with Cramer's condition II”, Siberian Mathematical Journal, 59:4 (2018), 731–750

[3] A.A. Mogulskii, E.I. Prokopenko, “Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. I”, Siberian Electronic Mathematical Reports, 15 (2018), 475–502

[4] A.A. Mogulskii, E.I. Prokopenko, “Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. II”, Siberian Electronic Mathematical Reports, 15 (2018), 503–527

[5] A.A. Mogulskii, E.I. Prokopenko, “Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. IV”, Siberian Electronic Mathematical Reports (to appear)