Geodesic
A remark on normalizations in a local large deviations principle for inhomogeneous birth -- and -- death process
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1258-1269

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This work is a continuation of [13]. We consider a continuous-time birth – and – death process in which the transition rates are regularly varying function of the process position. We establish rough exponential asymptotic for the probability that a sample path of a normalized process lies in a neighborhood of a given nonnegative continuous function. We propose a variety of normalization schemes for which the large deviation functional preserves its natural integral form.
Keywords: birth – and – death process, normalization (scaling), large deviations principle, local large deviations principle, rate function. 
@article{SEMR_2020_17_a50,
     author = {A. V. Logachov and Y. M. Suhov and N. D. Vvedenskaya and A. A. Yambartsev},
     title = {A remark on normalizations in a local large deviations principle for inhomogeneous birth -- and -- death process},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1258--1269},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a50/}
}
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A. V. Logachov; Y. M. Suhov; N. D. Vvedenskaya; A. A. Yambartsev. A remark on normalizations in a local large deviations principle for inhomogeneous birth -- and -- death process. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1258-1269. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a50/