4 citations · 4 across the 4 of their papers we have counts for
6 papers
On strong forms of the Borel--Cantelli lemma and intermittent interval maps
Andrei N. Frolov
We derive new variants of the quantitative Borel--Cantelli lemma and apply them to analysis of statistical properties for some dynamical systems. We consider intermittent maps of $…
On upper and lower bounds for probabilities of combinations of events
Andrei N. Frolov
We derive new upper and lower bounds for probabilities that or at least from events occur. These bounds can turn to equalities. The method is discussed as well. It work…
On large deviations for combinatorial sums
Andrei N. Frolov
We investigate asymptotic behaviour of probabilities of large deviations for normalized combinatorial sums. We find a zone in which these probabilities are equivalent to the tail o…
On lower and upper bounds for probabilities of unions and the Borel--Cantelli lemma
Andrei N. Frolov
We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary me…
Bounds of the remainder in a combinatorial central limit theorem
Andrei N. Frolov
We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random vari…
Small deviations of iterated processes in space of trajectories
Andrei N. Frolov
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincid…