The local principle of large deviations for solutions of Itô stochastic equations with quick drift

Logachov, A. V.

doi:10.1007/s10958-016-3008-6

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Cited by 3 publications

(2 citation statements)

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“…Note that the case m = 1, l = 0, follows from [10] (where a two dimensional Markov process is treated). A similar result is obtained in [24] for solutions of stochastic differential…”

Section: Introductionsupporting

confidence: 83%

A Local Large Deviation Principle for Inhomogeneous Birth–Death Processes

et al. 2018

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“…Note that the case m = 1, l = 0, follows from [10] (where a two dimensional Markov process is treated). A similar result is obtained in [24] for solutions of stochastic differential…”

Section: Introductionsupporting

confidence: 83%

A Local Large Deviation Principle for Inhomogeneous Birth–Death Processes

et al. 2018

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“…The idea and the method of proof goes back to [4,7,8]; this provides certain limitations for the parameters of the scheme. We would like to note that the case l = m is not covered by our condition (2) and hence is not considered in this paper, although it was included in [7] in a more specific situation.…”

Section: Introductionmentioning

confidence: 99%

A remark on normalizations in a local principle of large deviations

Logachov,

Suhov,

Vvedenskaya

et al. 2019

Preprint

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This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. 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.

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