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math.ST2021★ 1 cited
The roughness exponent and its model-free estimation
Xiyue Han, Alexander Schied
Motivated by pathwise stochastic calculus, we say that a continuous real-valued function admits the roughness exponent if the variation of converges to…
math.PR2021
A limit theorem for Bernoulli convolutions and the -variation of functions in the Takagi class
Xiyue Han, Alexander Schied, Zhenyuan Zhang
We consider a probabilistic approach to compute the Wiener--Young -variation of fractal functions in the Takagi class. Here, the -variation is understood as a generalization…