Geodesic
Renewal theorems in $R^d$
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 565-573

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Let $\zeta_n$ be the sum of i. i. d. random vectors. The renewal measure $\displaystyle H(E)=\sum_{n=1}^{\infty}\mathbf P\{\zeta_n\in E\}$ with $E$ being a bounded Borel set is considered. Some results concerning the asymptotic behaviour of $H(E+x)$ as $|x|\to\infty$ are obtained. 
@article{TVP_1979_24_3_a9,
     author = {A. V. Nagaev},
     title = {Renewal theorems in $R^d$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {565--573},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a9/}
}
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A. V. Nagaev. Renewal theorems in $R^d$. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 565-573. http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a9/