Geodesic
Large deviations for processes on half-line: Random Walk and Compound Poisson Process
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1-20

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We establish, under the Cramer exponential moment condition in a neighbourhood of zero, the Extended Large Deviation Principle for the Random Walk and the Compound Poisson processes in the metric space $\mathbb{V}$ of functions of finite variation on $[0,\infty)$ with the modified Borovkov metric.
Keywords: Large Deviations, Random Walk, Compound Poisson Process, Cramer's condition, rate function, Extended Large Deviation Principle. 
@article{SEMR_2019_16_a37,
     author = {F. C. Klebaner and A. A. Mogulskii},
     title = {Large deviations for processes on half-line: {Random} {Walk} and {Compound} {Poisson} {Process}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1--20},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a37/}
}
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F. C. Klebaner; A. A. Mogulskii. Large deviations for processes on half-line: Random Walk and Compound Poisson Process. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1-20. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a37/