Xīlíng Zhāng
张熙泠
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Photo taken on Bruach na Frìthe, Isle of Skye.
I am a teaching lecturer at the School of Mathematics, University of Leeds, UK.
Previously I worked at the University of Leicester as a teaching fellow (2023-2024), and before that I was a postdoc at Illinois Institute of Technology, Chicago (2019-2022), where my research mentor was Sergey Nadtochiy. I started my career as a university teacher at the University of Edinburgh (2017-2019), from which I received my doctorate (2017). My thesis advisor was Prof. Sandy Davie.
I am interested in probability and stochastic analysis, with particular focuses on the following topics:
Probabilisitic methods for free-boundary problems, especially the super-cooled Stefan problem.
Scaling limits of diffusion-limited aggregations.
Mean-field limits of integrate-and-fire models for neuronal networks (computational neuroscience).
Numerical approximations for stochastic differential equations.
Probabilistic applications of optimal transport, especially the coupling method for diffusion approximations, sharp bounds for the central limit theorem, etc.
Papers
Singular Heterogeneous Integrate-and-fire Model with Inhibitory Synapses
with Sergey Nadtochiy, work in progress.Scaling Limits of External Multi-particle DLA on the Plane and the Supercooled Stefan Problem
with Sergey Nadtochiy and Mykhaylo Shkolnikov, Ann. Inst. H. Poincaré Probab. Statist. 60(1): 658-691 (February 2024).A Coupling for Triple Stochastic Integrals
Nov 2019. arXiv:1811.11559.A Multi-Dimensional Central Limit Bound and Its Application to Euler’s Approximation of Lévy-SDEs
ESAIM: PS 23 (2019) 112–135.V-Integrability, Asymptotic Stability and Comparison Property of Explicit Numerical Schemes for Non-Linear SDEs
with Łukasz Szpruch, Mathematics of Computations (2017), vol. 87, no. 310, pp. 755-783.
I have also reviewed papers for the following journals:
Annals of Applied Probability
Proceedings of the International Colloquium on Backward Stochastic Differential Equation
Journal of Computational and Applied Mathematics
Journal of Computational Mathematics
Talks
11/2024: University of Leeds
Probability Seminar11/2023: London School of Economics and Political Science
Joint Risks & Stochastics and Financial Mathematics Seminar11/2020: Illinois Institute of technology, Chicago
Seminar on Mathematical Finance, Stochastic Analysis and Machine Learning11/2018: University of Edinburgh
Workshop on Wasserstein Calculus and Related Topics09/2018: University of Edinburgh
North British Probability Seminar07/2017: University of Edinburgh
International Workshop on BSDEs, SPDEs and their Applications06/2016: Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Spain
3rd Barcelona Summer School on Stochastic Analysis12/2014: Heriot-Watt University, Edinburgh, UK
Probability Day
MSc Projects
University of Leeds
2024
Thuraya Aldawsari, Zige Cheng, Xinyuan Han, Wenhan Li. Using Random Walks in Exchange Rate Modelling.
University of Edinburgh
2019
Zhixuan Liu, Strong Convergence and Stability of the Euler Approximations for Interest Rate Models.
Puwei Zhang, Option Pricing via the Milstein Scheme and Multilevel Monte Carlo Method.
Huiyu Zhang, Option Prices under Different Pricing Measures in the Stochastic Volatility Model.
2018
Yue Fan, European-type option pricing via the Lévy noise.
Siya Gao, Multi-level Monte Carlo simulation for interest rate models with small jumps.
Jun Liu, The θ-method for stochastic differential equations with jumps.
Yuting Yang, Pricing the passport option via local time.
2017
Xin Guan, Analysis and simulation of implicit methods for jump-diffusion models.
Shiyu Ma, Simulation of interest rate models with jumps.
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