Yi Shen
Research Interests
My main research area is applied probability. Currently I focus on understanding the relation between the random locations (e.g., the location of the path supremum, the hitting times, etc.) and the probabilistic symmetries of stochastic processes/random fields, such as stationarity, self-similarity, exchangeability, etc. I am also working on characterizing these symmetries using various tools including extreme value theory and ergodic theory.
More generally, I am enthusiastic about various problems in probability, such as random algebraic topology, limit theorems and financial mathematics. I am also interested in the applications of probability in statistics, physics, econometrics and actuarial science.
Education/biography
- 2013 PhD (Operations Research) Cornell University, U.S.A. Advisor: Gennady Samorodnitsky.
- 2008 Ingenieur (Quantitative Economics and Finance) Ecole Polytechnique, France.
- 2005 BS (Mathematics and Physics) Tsinghua University, China.
Professor Shen has joined the Department of Statistics and Actuarial Science at the University of Waterloo since July, 2013 as an assistant professor.
Selected publications
- Shen, J., Shen, Y., Wang, B. and Wang, R. Distributional compatibility for change of measures. Finance and Stochastics, accepted.
- Shen, Y. and Wang, Y. Operator-scaling Gaussian random fields via aggregation. Bernoulli, accepted.
- Shen, Y. and Wirjanto, T. S. Stationarity as a path property. Probability and Mathematical Statistics, accepted.
- Shen, J., Shen, Y. and Wang, R. Random Locations of Periodic Stationary Processes. Stochastic Processes and their Applications, 129(3), 878-901, 2019.
- Shen, Y. Location of the path supremum for self-similar processes with stationary increments. Annales de l'Institut Henri Poincaré, 54(4), 2349-2360, 2018.
- Lu, S., Huang, S., Li, K., Li, J., Chen, J., Ji, Z., Shen, Y., Zhou, D., Zeng, B. A Separability-Entanglement Classifier via Machine Learning. Physical Review A 98, 012315, 2018.
- Pei, Z. and Shen, Y. The devil is in the tails: regression discontinuity design with measurement error in the assignment variable. Advances in Econometrics Vol. 38. Regression Discontinuity Designs: Theory and Applications 455-502, 2017.
- Shen, Y. Random locations, ordered random sets and stationarity. Stochastic Processes and their Applications 126:3, 906-929, 2016.
- Chen, J., Ji, Z., Liu, Z., Shen, Y. and Zeng, B. Geometry of reduced density matrices for symmetry-protected topological phase. Physical Review A 93, 012309, 2016.
- Chen, J., Ji, Z., Li, C-K., Poon, Y-T., Shen, Y., Yu, N., Zeng, B. and Zhou, D. Discontinuity of maximum entropy inference and quantum phase transitions. New Journal of Physics 17 083019, 2015.
- Samorodnitsky, G. and Shen, Y. Intrinsic location functionals of stationary processes. Stochastic Processes and their Applications 123:11, 4040-4064, 2013.
- Samorodnitsky, G. and Shen, Y. Is the location of the supremum of a stationary process nearly uniformly distributed? Annals of Probability 41:5, 3494-3517, 2013.
- Samorodnitsky, G. and Shen, Y. Distribution of the supremum location of stationary processes. Electronic Journal of Probability 17:42, 1-17, 2012.