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Journal Article
Stochastics and Dynamics, ISSN 0219-4937, 2014, Volume 14, Issue 2, pp. 1350021 - 1-1350021-30
Journal Article
Physical Review Letters, ISSN 0031-9007, 05/2010, Volume 104, Issue 21, p. 211601
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 2015, Volume 28, Issue 1, pp. 137 - 183
In this paper, we obtain almost sure invariance principles with rate of order , , for sums associated with a sequence of reverse martingale differences... 
Strong invariance principle | Expanding maps | Smooth dynamical systems | Reverse martingale | MODERATE DEVIATIONS | BROWNIAN-MOTION | STATISTICS & PROBABILITY | UNBOUNDED FUNCTIONS | ITERATED LOGARITHM | RANDOM-VARIABLES | CENTRAL LIMIT-THEOREMS | INDEPENDENT RVS | STATIONARY-PROCESSES | DYNAMICAL-SYSTEMS | PARTIAL-SUMS | Probability | Mathematics
Journal Article
Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 2014, Volume 50, Issue 3, pp. 872 - 898
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective... 
Markov chains | Quenched central limit theorem | Weak invariance principle | Strong mixing | TRANSITION | CRITERIA | MARTINGALE APPROXIMATIONS | MARKOV-CHAINS | STATISTICS & PROBABILITY | CENTRAL-LIMIT-THEOREM | SUMS | Probability | Mathematics | 60J05 | 60F17 | 60F05
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 11/2019, Volume 129, Issue 11, pp. 4500 - 4509
The St. Petersburg paradox (Bernoulli, 1738) concerns the fair entry fee in a game where the winnings are distributed as P(X=2k)=2−k,k=1,2,…. The tails of X... 
Strong approximation | St. Petersburg sums | Central limit theorem | Semistable process | SURE | INVARIANCE-PRINCIPLES | STATISTICS & PROBABILITY
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 2011, Volume 1343, Issue 1, pp. 545 - 547
Conference Proceeding
The Annals of probability, ISSN 0091-1798, 3/2005, Volume 33, Issue 2, pp. 823 - 840
Journal Article
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 12/2006, Volume 19, Issue 3, pp. 647 - 689
Journal Article
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 04/2018, Volume 128, Issue 4, pp. 1347 - 1385
The famous results of Komlós, Major and Tusnády (see Komlós et al., 1976 [15] and Major, 1976 [17]) state that it is possible to approximate almost surely the... 
Strong invariance principle | KMT approximation | Markov chains | Random iterates | Left random walk on [formula omitted] | Left random walk on GL | R | Left random walk on GL(d)(R) | INEQUALITY | STATISTICS & PROBABILITY | STATIONARY-SEQUENCES | DEPENDENCE | INDEPENDENT RVS | WEAK INVARIANCE-PRINCIPLE | PARTIAL-SUMS | CENTRAL-LIMIT-THEOREM | Markov processes | Analysis
Journal Article
STOCHASTICS AND DYNAMICS, ISSN 0219-4937, 02/2020, Volume 20, Issue 1
For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O ((log... 
Markov chain | STRONG APPROXIMATION | PARTIAL SUMS | DECAY | Strong invariance principle | KMT approximation | STATISTICS & PROBABILITY | nonuniformly expanding dynamical systems | RANDOM-VARIABLES | KOMLOS
Journal Article
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