Geodesic
Extension of the invariance principle for compound renewal processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 651-670

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The invariance principle for compound renewal processes is extended (in the sense of asymptotic equivalence) to the zone of moderately large and small deviations. It is assumed that the vector $(\tau,\zeta)$, which “governs” the process, satisfies certain moment conditions (for example, the Cramér condition), and its components $\tau$ and $\zeta$ are either independent or linearly dependent. This extension holds, in particular, for random walks.
Keywords: compound renewal process, invariance principle, large deviations, small deviations, random walk. 
@article{TVP_2020_65_4_a0,
     author = {A. A. Borovkov},
     title = {Extension of the invariance principle for compound renewal processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {651--670},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a0/}
}
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A. A. Borovkov. Extension of the invariance principle for compound renewal processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 651-670. http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a0/