scholarly journals Invariance principle for stochastic processes with short memory

2006 ◽  
pp. 18-32 ◽  
Author(s):  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Stochastic Processes ◽  
Invariance Principle ◽  
Short Memory

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.

ON THE INVARIANCE PRINCIPLE UNDER MARTINGALE APPROXIMATION

2011 ◽  
Vol 11 (01) ◽  
pp. 95-105 ◽  
Author(s):  
MAGDA PELIGRAD ◽  
COSTEL PELIGRAD
Keyword(s):  
Markov Chain ◽  
Stochastic Processes ◽  
Invariance Principle ◽  
Normal Operator ◽  
Random Variables ◽  
Partial Sums ◽  
Linear Combinations ◽  
Additive Functionals ◽  
Martingale Approximation

In this paper, we establish continuous Gaussian limits for stochastic processes associated to linear combinations of partial sums. The underlying sequence of random variables is supposed to admit a martingale approximation in the square mean. The results are useful in studying averages of additive functionals of a Markov chain with normal operator.

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