Large and moderate deviations for the left random walk on GLd(R) | Zendy

Christophe Cuny | Zendy; Jérôme Dedecker | Zendy; Florence Merlevède | Zendy

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Large and moderate deviations for the left random walk on GLd(R)

Author(s) -

Christophe Cuny,

Jérôme Dedecker,

Florence Merlevède

Publication year - 2017

Publication title -

latin american journal of probability and mathematical statistics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.667

H-Index - 18

ISSN - 1980-0436

DOI - 10.30757/alea.v14-26

Subject(s) - mathematics , martingale (probability theory) , large deviations theory , independent and identically distributed random variables , moment (physics) , exponential function , order (exchange) , random walk , standard deviation , random variable , statistical physics , mathematical analysis , statistics , physics , economics , finance , classical mechanics

Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential moments to weak moments of order p u003e 1, to get a complete picture of the situation. We also prove a moderate deviation principle under an appropriate tail condition.

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