Geodesic
Large deviation principle for multidimensional first compound renewal processes in the phase space
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1464-1477

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We obtain the large deviation principles for multidimensional first compound renewal processes $\mathbf{Z}(t)$ in the phase space $\mathbb{R}^d$, for this we find and investigate the rate function $D_Z(\alpha)$. Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function $A_Z(\mu)$.
Keywords: compound multidimensional renewal process, large deviations, renewal measure, Cramer's condition, deviation (rate) function, second deviation (rate) function, fundamental function. 
@article{SEMR_2019_16_a42,
     author = {A. A. Mogulskii and E. I. Prokopenko},
     title = {Large deviation principle for multidimensional first compound renewal processes in the phase space},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1464--1477},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a42/}
}
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A. A. Mogulskii; E. I. Prokopenko. Large deviation principle for multidimensional first compound renewal processes in the phase space. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1464-1477. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a42/