Large Deviations and Statistical Invariance Principle

1993 ◽  
Vol 37 (1) ◽  
pp. 7-13 ◽  
Author(s):  
A. A. Borovkov ◽  
A. A. Mogulskii
Keyword(s):  
Large Deviations ◽  
Invariance Principle

MARTINGALE APPROXIMATION OF NON-STATIONARY STOCHASTIC PROCESSES

2006 ◽  
Vol 06 (02) ◽  
pp. 173-183 ◽  
Author(s):  
DALIBOR VOLNÝ
Keyword(s):  
Large Deviations ◽  
Stochastic Processes ◽  
Discrete Time ◽  
Invariance Principle ◽  
Limit Theorems ◽  
Orlicz Spaces ◽  
Stationary Case ◽  
Martingale Approximation ◽  
Stationary Stochastic Processes ◽  
Log Law

We generalise the martingale-coboundary representation of discrete time stochastic processes to the non-stationary case and to random variables in Orlicz spaces. Related limit theorems (CLT, invariance principle, log–log law, probabilities of large deviations) are studied.

Martingale-coboundary representation for stationary random fields

2017 ◽  
Vol 18 (02) ◽  
pp. 1850011 ◽  
Author(s):  
Dalibor Volný
Keyword(s):  
Large Deviations ◽  
Invariance Principle ◽  
Random Fields ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
One Dimensional ◽  
Weak Invariance Principle ◽  
Weak Invariance ◽  
Dimension One ◽  
Necessary And Sufficient

We prove a martingale-coboundary representation for random fields with a completely commuting filtration. For random variables in [Formula: see text], we present a necessary and sufficient condition which is a generalization of Heyde’s condition for one-dimensional processes from 1975. For [Formula: see text] spaces with [Formula: see text] we give a necessary and sufficient condition which extends Volný’s result from 1993 to random fields and improves condition of El Machkouri and Giraudo from 2016. A new sufficient condition is presented which for dimension one improves Gordin’s condition from 1969. In application, new weak invariance principle and estimates of large deviations are found.

scholarly journals A deviation bound for α-dependent sequences with applications to intermittent maps

2016 ◽  
Vol 17 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Jérôme Dedecker ◽  
Florence Merlevède
Keyword(s):  
Large Deviations ◽  
Invariance Principle ◽  
Upper Bounds ◽  
Partial Sums ◽  
Rosenthal Inequality ◽  
Deviation Inequality ◽  
Mixing Sequences

We prove a deviation bound for the maximum of partial sums of functions of [Formula: see text]-dependent sequences as defined in [2]. As a consequence, we extend the Rosenthal inequality of Rio [16] for [Formula: see text]-mixing sequences in the sense of Rosenblatt [18] to the larger class of [Formula: see text]-dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and Hölderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not [Formula: see text]-mixing in the sense of Rosenblatt.

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