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On Small Deviation Asymptotics in $L_2$ of Some Mixed Gaussian Processes. / Назаров, Александр Ильич; Никитин, Яков Юрьевич.

In: Mathematics, Vol. 6, No. 4, 55, 04.2018.

Research output: Contribution to journal › Article › peer-review

Harvard

Назаров, АИ & Никитин, ЯЮ 2018, 'On Small Deviation Asymptotics in $L_2$ of Some Mixed Gaussian Processes', Mathematics, vol. 6, no. 4, 55. https://doi.org/10.3390/math6040055

APA

Назаров, А. И., & Никитин, Я. Ю. (2018). On Small Deviation Asymptotics in $L_2$ of Some Mixed Gaussian Processes. Mathematics, 6(4), [55]. https://doi.org/10.3390/math6040055

Vancouver

Назаров АИ, Никитин ЯЮ. On Small Deviation Asymptotics in $L_2$ of Some Mixed Gaussian Processes. Mathematics. 2018 Apr;6(4). 55. https://doi.org/10.3390/math6040055

Author

Назаров, Александр Ильич ; Никитин, Яков Юрьевич. / On Small Deviation Asymptotics in $L_2$ of Some Mixed Gaussian Processes. In: Mathematics. 2018 ; Vol. 6, No. 4.

BibTeX

@article{a9d84864d3a9496199809e112cc6c2c3,
title = "On Small Deviation Asymptotics in $L_2$ of Some Mixed Gaussian Processes",
abstract = "We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of theWiener process and the Brownian bridge.We get the precise final result in this case and in some examples of more complicated processes of similar structure. The proof is based on Karhunen-Lo{\`e}ve expansion together with spectral asymptotics of differential operators and complex analysis methods.",
keywords = "дробное броуновское движение, гильбертова норма, малые уклонения случайных процессов, Mixed Gaussian process, Exact asymptotics, Small deviations, small deviations, FRACTIONAL BROWNIAN-MOTION, BOUNDARY-VALUE-PROBLEMS, RESPECT, exact asymptotics, NORM, FUNCTIONAL-INTEGRALS, mixed Gaussian process",
author = "Назаров, {Александр Ильич} and Никитин, {Яков Юрьевич}",
year = "2018",
month = apr,
doi = "10.3390/math6040055",
language = "English",
volume = "6",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "4",

}

RIS

TY - JOUR

T1 - On Small Deviation Asymptotics in $L_2$ of Some Mixed Gaussian Processes

AU - Назаров, Александр Ильич

AU - Никитин, Яков Юрьевич

PY - 2018/4

Y1 - 2018/4

N2 - We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of theWiener process and the Brownian bridge.We get the precise final result in this case and in some examples of more complicated processes of similar structure. The proof is based on Karhunen-Loève expansion together with spectral asymptotics of differential operators and complex analysis methods.

AB - We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of theWiener process and the Brownian bridge.We get the precise final result in this case and in some examples of more complicated processes of similar structure. The proof is based on Karhunen-Loève expansion together with spectral asymptotics of differential operators and complex analysis methods.

KW - дробное броуновское движение

KW - гильбертова норма

KW - малые уклонения случайных процессов

KW - Mixed Gaussian process

KW - Exact asymptotics

KW - Small deviations

KW - small deviations

KW - FRACTIONAL BROWNIAN-MOTION

KW - BOUNDARY-VALUE-PROBLEMS

KW - RESPECT

KW - exact asymptotics

KW - NORM

KW - FUNCTIONAL-INTEGRALS

KW - mixed Gaussian process

UR - http://www.scopus.com/inward/record.url?scp=85045104621&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/small-deviation-asymptotics-linf2infof-some-mixed-gaussian-processes

U2 - 10.3390/math6040055

DO - 10.3390/math6040055

M3 - Article

VL - 6

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 4

M1 - 55

ER -

ID: 18082952