Geodesic
The rate function and the fundamental function for multidimensional compound renewal process
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1449-1463

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We consider two multidimensional compound renewal processes $\mathbf{Z}(t)$ and $\mathbf{Y}(t)$. Assuming that the increments satisfy the Cramer's condition, we define and investigate the rate functions and the fundamental functions for the processes $\mathbf{Z}(t)$ and $\mathbf{Y}(t)$.
Keywords: compound multidimensional renewal process, large deviations, Cramer's condition, deviation (rate) function, fundamental function
Mots-clés : Legendre transformation. 
@article{SEMR_2019_16_a41,
     author = {A. A. Mogulskii and E. I. Prokopenko},
     title = {The rate function and the fundamental function for multidimensional compound renewal process},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1449--1463},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a41/}
}
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A. A. Mogulskii; E. I. Prokopenko. The rate function and the fundamental function for multidimensional compound renewal process. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1449-1463. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a41/