Yuan-Chung Sheu ( 中文版 )

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Professor of Applied Mathematics

Contact information Email : sheu@math.nctu.edu.tw Tel : +886-3-571-2121 ext. 56428 Fax : +886-3-572-4679 Address : Department of Applied mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan 30050.

Teaching

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• 2025 Fall Semester：
• Calculus (I)
• Probability Theory (I)
• 2026 Spring Semester：
• Calculus (II)
• Probability Theory (II)

Links :

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• Notices of the American Mathematical Society
• Fields Medal-IMU Awards
• Abel Prize Laureates
• Nobel Prizes and Laureates
• undergraduate level：
• Lecture Notes for Math 151 by Sourav Chatterjee
• Introduction to Probability Theory by Dmitry Panchenko
• Introduction to Stochastic Processes by Gregory F. Lawler
• A First Course in Stochastic Calculus by Louis-Pierre Arguin
• High-Dimensional Probability: An Introduction with Applications in Data Science by Roman Vershynin
• graduate level：
• Knowing the Odds: An Introduction to Probability, by John B. Walsh
• Measure Theory, Probability, and Stochastic Processes, by J. F. Le Gall
• Graduate Probability (Stats 310 Series) by Sourav Chatterjee
• Brownian Motion, Martingales, and Stochastic Calculus by J. F. Le Gall
• Stochastic Partial Differential Equations, Space-time White Noise and Random Fields by Robert C.Dalang and Marta Sanz-Sole'
• An Introduction to SPDEs by Martin Hairer
• Upper and Lower bounds for Stochastic Processes : Decomposition Theorems by Michel Talagrand
• Others：
• Localization, Delocalization, and Diffusion in Disordered Systems, Videos from BIRS Workshop
• 2026 NCTS Workshop on Probability and Its Applications


Vitae

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• Education
• Ph.D. in Mathematics, Cornell University, 1993.
• Research Areas
• Probability Theory and its Applications.
• Positions, Honors and Awards
• Associate Professor of Mathematics, NCTU, 1993~1998
• Professor of Mathematics, NCTU, 1999~
• General Member, MSRI at Berkeley, 1997~1998
• Chair, Mathematics Department, NCTU, 2001~2003
• Associate Editor, Taiwanese Journal of Mathematics, 2004~2013
• Visiting Scholar, University of Washington, Seattle, USA, 2006~2007
• Associate Dean, College of Science, NCTU, 2005~2006, 2007~2008
• Vice President, Taiwanese Mathematical Society, 2012~2013
• Editor, Advances and Applications in Statistics, 2012~2021


Publications

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1. Probabilistic Analysis for Scalogram Ridges in Signal Processing (jointly with Gi-Ren Liu and Hau-Tieng Wu), Quarterly of Applied Mathematics 84 (2026), 465-521
2. On random fields associated with analytic wavelet transform (jointly with Gi-Ren Liu and Hau-Tieng Wu), IEEE Transactions on Information Theory, Vol. 72, No. 3, pp. 2005-2027, March 2026
3. Gaussian Approximation for the Moving Averaged Modulus Wavelet Transform and its Variants (jointly with Gi-Ren Liu and Hau-Tieng Wu), Applied and Computational Harmonic Analysis, Vol.74, January 2025
4. Model-based assessment of photoplethysmogram signal quality in real-life environments (jointly with Yan-Wei Su, Chia-Cheng Hao, Gi-Ren Liu and Hau-Tieng Wu) 2024 32nd European Signal Processing Conference (EUSIPCO), 1726-1730, 2024
5. Ridge detection for nonstationary multicomponent signals with time-varying wave-shape functions and its applications (jointly with Yan-Wei Su, Gi-Ren Liu and Hau-Tieng Wu), IEEE Transactions on Signal Processing, Vol.72, 4843-4854, 2024
6. Reconsider photoplethysmogram signal quality assessment in the free living environment (jointly with Yan-Wei Su, Chia-Cheng Hao, Gi-Ren Liu and Hau-Tieng Wu), Physiological Measurement 45(6),06NT01(2024), Link
7. When Scattering Transform Meets Non-Gaussian Random Processes, a Scaling Limit Result(jointly with Gi-Ren Liu and Hau-Tieng Wu), Bernoulli 30(3): 2346-2371 (August 2024)
8. Matrix Deviation Inequality for lp-Norm (jointly with Te-Chun Wang), Random Matrices:Theory and Applications Vol. 12, No. 4 (2023) Link
9. Central and Non-central Limit Theorems arising from the Scattering Transform and its Neural Activation Generalization (jointly with Gi-Ren Liu and Hau-Tieng Wu) SIAM Journal on Mathematical Analysis 55 (2) 1170-1213 (2023) Link (Early version, 53 pages)
10. Asymptotic Analysis of Higher-order Scattering Transform of Gaussian Processes (jointly with Gi-Ren Liu and Hau-Tieng Wu) Electronic Journal of Probability, Vol. 27, paper no. 48, 1-27 (2022) Link
11. Large scale assesment of consistency in sleep stage scoring rules among multiple sleep centers using an interpretable machine learning algorithm (jointly with Gi-Ren Liu, Yu-Lun Lo, Hau-Tieng Wu and et al.) Journal of Clinical Sleep Medicine, Vol. 17, No 2 (2021), 159-166
12. Save muscle information - unfiltered EEG signal helps distinguish sleep stages (jointly with C. Lustenberger, Y. L. Lo, W. T. Liu and H. T. Wu) Sensors 20 (2020).
13. Explore intrinsic geometry of sleep dynamics and predict sleep stage by unsupervised learning techniques (jointly with Gi-Ren Liu, Yu-Lun Lo, Hau-Tieng Wu), Book chapter, Harmonic Analysis and Applications, Springer, 2021, 279-324.
14. Diffuse to fuse EEG spectra -- intrinsic geometry of sleep dynamics for classification (jointly with Gi-Ren Liu, Yu-Lun Lo, John Malik, Hau-tieng Wu), Biomedical Signal Processing and Control, 55 (2020), 101576.
15. The L2-Cutoff for reversible Markov Chain (jointly with Guan-Yu Chen and Jui-Ming Hsu). Annals of Applied Probability, 27, 2304-2341 (2017).
16. First exit from an open set for a matrix-valued Lévy process (jointly with Yu-Ting Chen and Yu-Tzu Chen), Statistics and Probability Letters, 127, 104-110 (2017).
17. Pricing perpetual American compound options under a matrix-expoenetial jump-diffusion model (jointly with Ming-Chi Chang and Ming-Yao Tsai), Applied Mathematical Finance, 22 (2015), 553-575.
18. Disorder chaos in the spherical mean-field model (jointly with Wei-Kuo Chen, Hsin-Wei Hsieh and Chi-Ruey Huaung), Journal of Statistical Physics (2015), 160; 417-729.
19. Free boundary problems and perpetual American strangles (jointly with Ming-Chi Chang), Quantitative Finance 13(2013), No.08, 1149-1155.
20. A note on Gerber-Shiu function for hyper-exponential jump-diffusion processes (jointly with Yu-Ting Chen and Ming-Chi Chang), Elect. Comm. in Probab.18 (2013), No.2, 1-8
21. The cutoff phenomenon for Ehrenfest chains (jointly with Guan-Yu Chen and Yang-Jen Fang). Stochastic Processes and Their Applications 122 (2012), 2830-2853.
22. On optimal stopping problems for matrix-exponential Lévy processes(jointly with Ming-Yao Tsai). Journal of Applied Probability, 49,531-548(2012).
23. On the discounted penalty at ruin in a jump-diffusion model, Taiwanese Journal of Mathematics, 14, 1337-1350(2010)(jointly with Yu-Ting Chen)
24. A Generalized Model for Optimum Future Hedge. Handbbok of Quantitative Finance and Accounting, Lee,Cheng-Few, Lee, John(Eds.), Springer, 873-852(2010).(jointly with Jang-Yi Lee, Kehluh Wang, and Cheng-Few Lee)
25. A note on r-balayages of matrix-exponetial Lévy processes, Elect. Comm. in Probab. 14(2009), 165-175 (jointly with Yu-Ting Chen)
26. A generalized renewal equation for two-sided jump-diffusion models, Stochastic Analysis and Applications, 27,897-910 (2009) (jointly with Yu-Ting Chen)
27. An integral equation approach for defaultable bond prices with applications to credit spreads, J. Appl. Prob. 46, 71-84 (2009). (jointly with Yu-Ting Chen and Cheng-Few Lee)
28. The least cost super replicating portfolio in the Boyle-Vorst discrete-time option pricing model with transaction costs. International Journal of Theoretical and Applied Finance, Vol. 11, No.1, 55-85(2008).(jointly with Guan-Yu Chen and Ken Palmer)
29. An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model, Finance and Stochastics, 11, 323-355 (2007). (jointly with Yu-Ting Chen and Cheng-Few Lee)
30. The least cost super replication portfolio for short puts and calls in Boyle-Vorst option pricing model with transition cost, Advances in Quantitative Analysis and Accounting, 5, 1-22 (2007) .(jointly with Guan-Yu Chen and Ken Palmer)
31. On the Log-Sobolev Constant for the Simple Random Walk on the n-cycle: The Even Cases, Journal of Functional Analysis, 202, 473-485 (2003).
32. A Hausdorff measure classification of polar lateral boundary sets for superdiffusions, Mathematical Proceedings of Cambridge Philosophical Society, 128, 549-560 (2000).
33. On a problem of Dynkin, Proceedings of the AMS, 127, 3721-3728 (1999).
34. Life time and compactness of range for super-Brownian motion with a general branching mechanism, Stochastic Processes and their Applications, 70, 129-141 (1997).
35. On states of exit measures for superdiffusions, Ann. Probab., 24, 268-279 (1996).
36. On positive solutions of some nonlinear differential equation-a probablistic approach, Stochastic Processes and their Applications, 59, 43-53 (1995)
37. Removable boundary singularities of solutions of some nonlinear differential equations, Duke Math., 74, 701-711 (1994)
38. Asymptotic behaviour of superprocesses, Stochastics and Stochastics Reports, Vol. 49, 239-252 (1994).
39. A Hausdroff measure classification of G-Polar sets for the superdiffusions, Probab. Theory Relat.Fields, 95, 521-533 (1993).










Update. 06/12/2026