@article {31470,
	title = {A limit theorem for Bernoulli convolutions and the Φ-variation of functions in the Takagi class},
	journal = { Journal of Theoretical Probability},
	volume = {35},
	year = {2022},
	month = {2022},
	pages = {2853{\textendash}2878},
	abstract = {We consider a probabilistic approach to compute the Wiener{\textendash}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\&nbsp;<i>p</i>th variation of a trajectory computed along the sequence of dyadic partitions of the unit interval. The functions Φ\&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\&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.},
	url = {https://link.springer.com/article/10.1007/s10959-022-01157-1},
	author = {Xiyue Han and Alexander Schied and Zhengyuan Zhang}
}
