TY - JOUR
T1 - A nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets
AU - Kifer, Yuri
PY - 2012/9
Y1 - 2012/9
N2 - We provide conditions which yield a strong law of large numbers for expressions of the form 1/Nσ n N=1F(X(q1(n)),.., X(q(n))) where X(n), n < 0's is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polinomial growth and certain regularity properties and q i, i > m are positive functions taking on integer values on integers with some growth conditions. Applying these results we study certain multifractal formalism type questions concerning Hausdorff dimensions of some sets of numbers with prescribed asymptotic frequencies of combinations of digits at places q 1(n),.., q ℓ(n).
AB - We provide conditions which yield a strong law of large numbers for expressions of the form 1/Nσ n N=1F(X(q1(n)),.., X(q(n))) where X(n), n < 0's is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polinomial growth and certain regularity properties and q i, i > m are positive functions taking on integer values on integers with some growth conditions. Applying these results we study certain multifractal formalism type questions concerning Hausdorff dimensions of some sets of numbers with prescribed asymptotic frequencies of combinations of digits at places q 1(n),.., q ℓ(n).
KW - dynamical systems
KW - mixingales
KW - nonconventional ergodic averages
KW - Strong law of large numbers
UR - http://www.scopus.com/inward/record.url?scp=84861052955&partnerID=8YFLogxK
U2 - 10.1142/S0219493711500237
DO - 10.1142/S0219493711500237
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AN - SCOPUS:84861052955
SN - 0219-4937
VL - 12
JO - Stochastics and Dynamics
JF - Stochastics and Dynamics
IS - 3
M1 - 1150023
ER -