<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>36</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></authors></contributors><titles><title><style face="normal" font="default" size="100%">Estimating the roughness exponent of stochastic volatility from discrete observations of the integrated variance</style></title><secondary-title><style face="normal" font="default" size="100%">arXiv:2307.02582</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2307.02582</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>36</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></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models</style></title><secondary-title><style face="normal" font="default" size="100%">arXiv:2504.09276</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">arXiv:2504.09276</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>36</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></authors></contributors><titles><title><style face="normal" font="default" size="100%">Universal portfolios in continuous time: an approach in pathwise Itô calculus</style></title><secondary-title><style face="normal" font="default" size="100%">arXiv:2504.11881</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">Submitted</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>36</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></authors></contributors><titles><title><style face="normal" font="default" size="100%">Robust Faber--Schauder approximation based on discrete observations of an antiderivative</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics of Operations Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">Accepted</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/pdf/2211.11907.pdf</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We study the problem of reconstructing the Faber--Schauder coefficients of a continuous function&amp;nbsp;f&amp;nbsp;from discrete observations of its antiderivative&amp;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.</style></abstract></record><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></authors></contributors><titles><title><style face="normal" font="default" size="100%">The roughness exponent and its model-free estimation</style></title><secondary-title><style face="normal" font="default" size="100%">The Annals of Applied Probability</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2025</style></year></dates><volume><style face="normal" font="default" size="100%">35</style></volume><pages><style face="normal" font="default" size="100%">1049-1082</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>36</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></authors></contributors><titles><title><style face="normal" font="default" size="100%">A criterion for absolute continuity relative to the law of fractional Brownian motion</style></title><secondary-title><style face="normal" font="default" size="100%">Electronic Communications in Probability</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><volume><style face="normal" font="default" size="100%">29</style></volume><pages><style face="normal" font="default" size="100%">1-10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><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></authors></contributors><titles><title><style face="normal" font="default" size="100%">The roughness exponent and its application in finance</style></title><secondary-title><style face="normal" font="default" size="100%">Ph.D. Thesis</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://uwspace.uwaterloo.ca/items/f3e75496-92c5-4a64-a9fd-d7676f6c036b</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><work-type><style face="normal" font="default" size="100%">PhD thesis</style></work-type></record><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><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></authors></contributors><titles><title><style face="normal" font="default" size="100%">Step Roots of Littlewood Polynomials and the Extrema of Functions in the Takagi Class</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematical Proceedings of the Cambridge Philosophical Society </style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">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</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">173</style></volume><pages><style face="normal" font="default" size="100%">591-618</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">3</style></issue></record><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></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Gladyshev theorem for trifractional Brownian motion and n-th order fractional Brownian motion</style></title><secondary-title><style face="normal" font="default" size="100%">Electronic Communications in Probability</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">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</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">1-12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">54</style></issue></record><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%">Zhenyuan Zhang</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A probabilistic approach to the Phi-variation of classical fractal functions with critical roughness</style></title><secondary-title><style face="normal" font="default" size="100%">Statistics &amp; Probability Letters</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.sciencedirect.com/science/article/pii/S0167715220302236</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">168</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">108950</style></issue></record></records></xml>