Geodesic
Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds.~II
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 503-527.

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In the work, which consists of 4 papers (the article and [1]–[3]), we obtain integro-local limit theorems in the phase space for multidimensional compound renewal processes, when Cramer's condition holds. In the part II (the article) we consider the so-called first renewal process $\mathbf{Z}(t)$ in an irregular region.
Keywords: compound multidimensional renewal process, first 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},
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A. A. Mogulskii; E. I. Prokopenko. Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds.~II. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 503-527. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a36/

[1] 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

[2] A.A. Mogulskii, E.I. Prokopenko, “Integro-local theorems for multidimensional compound renewal processes, when Cramer's condition holds. III”, Siberian Electronic Mathematical Reports, 15 (2018), 528–553

[3] 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)

[4] A.A. Mogulskii, E.I. Prokopenko, “Large deviation principle for multidimensional first compound renewal processes in phase space”, Siberian Electronic Mathematical Reports (to appear)

[5] R. Lefevere, M. Mariani, L. Zambotti, “Large deviations for renewal processes”, Stochastic Processes and their Applications, 121:10 (2011), 2243–2271 | DOI | MR | Zbl

[6] B. Tsirelson, “From uniform renewal theorem to uniform large and moderate deviations for renewal-reward processes”, Electron. Commun. Probab., 18 (2013), 52, 13 pp. | DOI | MR | Zbl

[7] 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

[8] 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

[9] M.A. Evgrafov, Analytic functions, Second Edition, Nauka, M., 1968 | MR | Zbl