@manuascript {35839,
	title = {Estimating the roughness exponent of stochastic volatility from discrete observations of the integrated variance},
	journal = {arXiv:2307.02582},
	year = {Submitted},
	url = {https://arxiv.org/abs/2307.02582},
	author = {Xiyue Han and Alexander Schied}
}
@manuascript {36763,
	title = {On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models},
	journal = {arXiv:2504.09276},
	year = {Submitted},
	url = {arXiv:2504.09276},
	author = {Xiyue Han and Alexander Schied}
}
@manuascript {36762,
	title = {Universal portfolios in continuous time: an approach in pathwise It{\^o} calculus},
	journal = {arXiv:2504.11881},
	year = {Submitted},
	author = {Xiyue Han and Alexander Schied}
}
@manuascript {31886,
	title = {Robust Faber--Schauder approximation based on discrete observations of an antiderivative},
	journal = {Mathematics of Operations Research},
	year = {Accepted},
	abstract = {We study the problem of reconstructing the Faber--Schauder coefficients of a continuous function\&nbsp;f\&nbsp;from discrete observations of its antiderivative\&nbsp;F. Our approach starts with formulating this problem through piecewise quadratic spline interpolation. We then provide a closed-form solution and an in-depth error analysis. These results lead to some surprising observations, which also throw new light on the classical topic of quadratic spline interpolation itself: They show that the well-known instabilities of this method can be located exclusively within the final generation of estimated Faber--Schauder coefficients, which suffer from non-locality and strong dependence on the initial value and the given data. By contrast, all other Faber--Schauder coefficients depend only locally on the data, are independent of the initial value, and admit uniform error bounds. We thus conclude that a robust and well-behaved estimator for our problem can be obtained by simply dropping the final-generation coefficients from the estimated Faber--Schauder coefficients.},
	url = {https://arxiv.org/pdf/2211.11907.pdf},
	author = {Xiyue Han and Alexander Schied}
}
@article {32782,
	title = {The roughness exponent and its model-free estimation},
	journal = {The Annals of Applied Probability},
	volume = {35},
	year = {2025},
	pages = {1049-1082},
	author = {Xiyue Han and Alexander Schied}
}
@manuascript {35837,
	title = {A criterion for absolute continuity relative to the law of fractional Brownian motion},
	journal = {Electronic Communications in Probability},
	volume = {29},
	year = {2024},
	pages = {1-10},
	author = {Xiyue Han and Alexander Schied}
}
@article {35836,
	title = {The roughness exponent and its application in finance},
	journal = {Ph.D. Thesis},
	year = {2024},
	type = {PhD thesis},
	url = {https://uwspace.uwaterloo.ca/items/f3e75496-92c5-4a64-a9fd-d7676f6c036b},
	author = {Xiyue Han}
}
@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}
}
@article {31469,
	title = {Step Roots of Littlewood Polynomials and the Extrema of Functions in the Takagi Class},
	journal = {Mathematical Proceedings of the Cambridge Philosophical Society },
	volume = {173},
	year = {2022},
	pages = {591-618},
	url = {https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/step-roots-of-littlewood-polynomials-and-the-extrema-of-functions-in-the-takagi-class/747DD5176BD8D0F4A226E5B09F876153},
	author = {Xiyue Han and Alexander Schied}
}
@article {31471,
	title = {A Gladyshev theorem for trifractional Brownian motion and n-th order fractional Brownian motion},
	journal = {Electronic Communications in Probability},
	volume = {26},
	year = {2021},
	pages = {1-12},
	url = {https://projecteuclid.org/journals/electronic-communications-in-probability/volume-26/issue-none/A-Gladyshev-theorem-for-trifractional-Brownian-motion-and-n-th/10.1214/21-ECP422.full},
	author = {Xiyue Han}
}
@article {30394,
	title = {A probabilistic approach to the Phi-variation of classical fractal functions with critical roughness},
	journal = {Statistics \& Probability Letters},
	volume = {168},
	year = {2021},
	url = {https://www.sciencedirect.com/science/article/pii/S0167715220302236},
	author = {Xiyue Han and Alexander Schied and Zhenyuan Zhang}
}
