On Lacunary Series with Random Gaps

TY - JOUR

T1 - On Lacunary Series with Random Gaps

AU - Raseta, M.

PY - 2014/10

Y1 - 2014/10

N2 - Abstract We prove Strassen's law of the iterated logarithm for sums (Formula presented.) where f is a smooth periodic function on the real line and (Formula presented.) is an increasing random sequence. Our results show that classical results of the theory of lacunary series remain valid for sequences with random gaps, even in the nonharmonic case and if the Hadamard gap condition fails.

AB - Abstract We prove Strassen's law of the iterated logarithm for sums (Formula presented.) where f is a smooth periodic function on the real line and (Formula presented.) is an increasing random sequence. Our results show that classical results of the theory of lacunary series remain valid for sequences with random gaps, even in the nonharmonic case and if the Hadamard gap condition fails.

UR - http://www.scopus.com/inward/record.url?scp=84902301811&partnerID=8YFLogxK

U2 - 10.1007/s10474-014-0430-4

DO - 10.1007/s10474-014-0430-4

M3 - Article

SN - 1588-2632

VL - 144

SP - 150

EP - 161

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1

ER -