The large deviation principle for certain series

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

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Abstract

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We study the large deviation principle for stochastic processes of the form $\left\{{\sum }_{k=1}^{\infty }{x}_{k}\left(t\right){\xi }_{k}:t\in T\right\}$, where ${\left\{{\xi }_{k}\right\}}_{k=1}^{\infty }$ is a sequence of i.i.d.r.v.'s with mean zero and ${x}_{k}\left(t\right)\in ℝ$. 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.

How to cite

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Arcones, Miguel A.. "The large deviation principle for certain series." ESAIM: Probability and Statistics 8 (2010): 200-220. <http://eudml.org/doc/104319>.

@article{Arcones2010,
abstract = { We study the large deviation principle for stochastic processes of the form $\\{\sum_\{k=1\}^\{\infty\}x_\{k\}(t)\xi_\{k\}:t\in T\\}$, where $\\{\xi_\{k\}\\}_\{k=1\}^\{\infty\}$ 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.; stochastic processes},
language = {eng},
month = {3},
pages = {200-220},
publisher = {EDP Sciences},
title = {The large deviation principle for certain series},
url = {http://eudml.org/doc/104319},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Arcones, Miguel A.
TI - The large deviation principle for certain series
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 200
EP - 220
AB - We study the large deviation principle for stochastic processes of the form $\{\sum_{k=1}^{\infty}x_{k}(t)\xi_{k}:t\in T\}$, where $\{\xi_{k}\}_{k=1}^{\infty}$ 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.; stochastic processes
UR - http://eudml.org/doc/104319
ER -

References

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