Geodesic
Integro-local limit theorems for compound renewal processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 217-240

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We obtain integro-local theorems (analogues of Stone's theorem) for compound renewal processes when at least one of the following two conditions is met: (a) the components of the jumps in the process are independent or are linearly dependent, or (b) the jumps have finite moments of an order higher than 2. In case (b) we obtain an upper bound for the remainder term.
Keywords: compound renewal process, integro-local theorem, analogues of Stone's theorem. 
@article{TVP_2017_62_2_a0,
     author = {A. A. Borovkov},
     title = {Integro-local limit theorems for compound renewal processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {217--240},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a0/}
}
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A. A. Borovkov. Integro-local limit theorems for compound renewal processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 217-240. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a0/