<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Xiyue Han</style></author><author><style face="normal" font="default" size="100%">Alexander Schied</style></author><author><style face="normal" font="default" size="100%">Zhengyuan Zhang</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A limit theorem for Bernoulli convolutions and the Φ-variation of functions in the Takagi class</style></title><secondary-title><style face="normal" font="default" size="100%"> Journal of Theoretical Probability</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2022</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/article/10.1007/s10959-022-01157-1</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">35</style></volume><pages><style face="normal" font="default" size="100%">2853–2878</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We consider a probabilistic approach to compute the Wiener–Young Φ-variation of fractal functions in the Takagi class. Here, the Φ-variation is understood as a generalization of the quadratic variation or, more generally, the&amp;nbsp;&lt;i&gt;p&lt;/i&gt;th variation of a trajectory computed along the sequence of dyadic partitions of the unit interval. The functions Φ&amp;nbsp;we consider form a very wide class of functions that are regularly varying at zero. Moreover, for each such function Φ, our results provide, in a straightforward manner, a large and tractable class of functions that have nontrivial and linear Φ-variation. As a corollary, we also construct stochastic processes whose sample paths have nontrivial, deterministic, and linear Φ-variation for each function Φ&amp;nbsp;from our class. The proof of our main result relies on a limit theorem for certain sums of Bernoulli random variables that converge to an infinite Bernoulli convolution.</style></abstract></record></records></xml>