# The large deviation principle for certain series

ESAIM: Probability and Statistics (2004)

- Volume: 8, page 200-220
- ISSN: 1292-8100

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topArcones, Miguel A.. "The large deviation principle for certain series." ESAIM: Probability and Statistics 8 (2004): 200-220. <http://eudml.org/doc/245701>.

@article{Arcones2004,

abstract = {We study the large deviation principle for stochastic processes of the form $\lbrace \sum _\{k=1\}^\{\infty \}x_\{k\}(t)\xi _\{k\}:t\in T\rbrace $, where $\lbrace \xi _\{k\}\rbrace _\{k=1\}^\{\infty \}$ is a sequence of i.i.d.r.v.’s with mean zero and $x_\{k\}(t)\in \mathbb \{R\}$. We present necessary and sufficient conditions for the large deviation principle for these stochastic processes in several situations. Our approach is based in showing the large deviation principle of the finite dimensional distributions and an exponential asymptotic equicontinuity condition. In order to get the exponential asymptotic equicontinuity condition, we derive new concentration inequalities, which are of independent interest.},

author = {Arcones, Miguel A.},

journal = {ESAIM: Probability and Statistics},

keywords = {large deviations; stochastic processes; Large deviations},

language = {eng},

pages = {200-220},

publisher = {EDP-Sciences},

title = {The large deviation principle for certain series},

url = {http://eudml.org/doc/245701},

volume = {8},

year = {2004},

}

TY - JOUR

AU - Arcones, Miguel A.

TI - The large deviation principle for certain series

JO - ESAIM: Probability and Statistics

PY - 2004

PB - EDP-Sciences

VL - 8

SP - 200

EP - 220

AB - We study the large deviation principle for stochastic processes of the form $\lbrace \sum _{k=1}^{\infty }x_{k}(t)\xi _{k}:t\in T\rbrace $, where $\lbrace \xi _{k}\rbrace _{k=1}^{\infty }$ is a sequence of i.i.d.r.v.’s with mean zero and $x_{k}(t)\in \mathbb {R}$. We present necessary and sufficient conditions for the large deviation principle for these stochastic processes in several situations. Our approach is based in showing the large deviation principle of the finite dimensional distributions and an exponential asymptotic equicontinuity condition. In order to get the exponential asymptotic equicontinuity condition, we derive new concentration inequalities, which are of independent interest.

LA - eng

KW - large deviations; stochastic processes; Large deviations

UR - http://eudml.org/doc/245701

ER -

## References

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