Staff profile

Employment and experience

Aug. 2020-present, Associate Professor, Department of Mathematical Sciences, Durham University, Durham, U.K.

Feb. 2019- July 2020, Senior Lecturer, Department of Mathematical Sciences, Loughborough University, Loughborough, U.K.

Oct. 2010- Jan. 2019, Lecturer, Department of Mathematical Sciences, Loughborough University, Loughborough, U.K.

Feb. 2009- Sept. 2010, Research Fellow, Department of Mathematical Sciences, Loughborough University, Loughborough, U.K

Aug. 2007- Sept. 2010, Lecturer, Department of Mathematics, Shanghai Jiao Tong University, Shanghai.

Grants

1.Jan. 2009 - Dec. 2009, National Natural Science Foundation of China (NSFC) funded Tian Yuan grant "Pathwise Property Analysis to Local Times and RDS", (PI).

2. Jan. 2010- Dec. 2010, Research Grant from Ministry of Education of China, (PI).

3. Jan. 2010 - Dec. 2012, NSFC funded project "Stochastic Differential Geometry and its application in Mathematical Finance", (CI).
4. June 2010, Collaborative small grants from London Mathematical Society (LMS) (Scheme 4) for Dr. L. Li, (PI).

5. 1 Mar. 2016 - 28 Feb. 2019, Royal Society Newton Advanced Fellowship Ergodicity of stochastic dynamical systems under nonlinear expectations, (CI).

6. Dec. 2016, Conference grant from LMS (Scheme 1) for "Stochastic Dynamical Systems and Ergodicity", London Mathematical Society, (PI).

7. Nov. 2018- Aug. 2020, East Midlands Stochastic Analysis Seminar (Loughborough, Oxford, Warwick, York), LMS, (PI).

8. Sept. 2020-Aug. 2021, North-East Midlands Stochastic Analysis Seminar (Durham, Oxford, Warwick, York), LMS, (PI).

PhD supervision

I have 9 completed PhDs and 1 on study.

• Stochastic analysis, stochastic (partial) differential equations, rough path, backward stochastic differential equations, random dynamical system, random periodic processes, ergodic theory, time series.

Journal Article

• Feng, C., Zhao, H., & Zhong, J. (2023). Existence of geometric ergodic periodic measures of stochastic differential equations. Journal of Differential Equations, 359, 67-106. https://doi.org/10.1016/j.jde.2023.02.022
• Feng, C., Liu, Y., & Zhao, H. (2023). Periodic measures and Wasserstein distance for analysing periodicity of time series datasets. Communications in Nonlinear Science and Numerical Simulation, 120, Article 107166. https://doi.org/10.1016/j.cnsns.2023.107166
• Feng, C., & Li, L. (2022). Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces. Advances in operator theory, 7, Article 5. https://doi.org/10.1007/s43036-021-00170-1
• Feng, C., Liu, Y., & Zhao, H. (2021). Ergodic Numerical Approximation to Periodic Measures of Stochastic Differential Equations. Journal of Computational and Applied Mathematics, 398, Article 113701. https://doi.org/10.1016/j.cam.2021.113701
• Feng, C., Qu, B., & Zhao, H. (2021). Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations. Journal of Differential Equations, 286, 119-163. https://doi.org/10.1016/j.jde.2021.03.022
• Feng, C., Zhao, H., & Zhong, J. (2021). Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance. Physica D: Nonlinear Phenomena, 417, https://doi.org/10.1016/j.physd.2020.132815
• Feng, C., & Zhao, H. (2021). Ergodicity of Sublinear Markovian Semigroups. SIAM Journal on Mathematical Analysis, 53(5), 5646-5681. https://doi.org/10.1137/20m1356518
• Feng, C., & Zhao, H. (2020). Random periodic processes, periodic measures and ergodicity. Journal of Differential Equations, 269(9), 7382-7428. https://doi.org/10.1016/j.jde.2020.05.034
• Feng, C., Qu, B., & Zhao, H. (2020). A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations. Nonlinearity, 33(10), https://doi.org/10.1088/1361-6544/ab9584
• Feng, C., Wu, P., & Zhao, H. (2020). Ergodicity of invariant capacities. Stochastic Processes and their Applications, 130(8), https://doi.org/10.1016/j.spa.2020.02.010
• Feng, C., Wang, X., & Zhao, H. (2018). Quasi-linear PDEs and forward–backward stochastic differential equations: Weak solutions. Journal of Differential Equations, 264(2), https://doi.org/10.1016/j.jde.2017.09.030
• Feng, C., Liu, Y., & Zhao, H. (2017). Numerical approximation of random periodic solutions of stochastic differential equations. Zeitschrift für angewandte Mathematik und Physik, 68(5), https://doi.org/10.1007/s00033-017-0868-7
• Feng, C., Wu, Y., & Zhao, H. (2016). Anticipating random periodic solutions—I. SDEs with multiplicative linear noise. Journal of Functional Analysis, 271(2), https://doi.org/10.1016/j.jfa.2016.04.027
• Feng, C., & Li, L. (2013). On the Móri-Székely conjectures for the Borel-Cantelli lemma. Studia Scientiarum Mathematicarum Hungarica, 50(2), https://doi.org/10.1556/sscmath.50.2013.2.1241
• Feng, C., & Zhao, H. (2012). Random periodic solutions of SPDEs via integral equations and Wiener–Sobolev compact embedding. Journal of Functional Analysis, 262(10), https://doi.org/10.1016/j.jfa.2012.02.024
• Feng, C., Zhao, H., & Zhou, B. (2011). Pathwise random periodic solutions of stochastic differential equations. Journal of Differential Equations, 251(1), https://doi.org/10.1016/j.jde.2011.03.019
• Feng, C., & Zhao, H. (2010). Local Time Rough Path for Lévy Processes. Electronic Journal of Probability, 15, https://doi.org/10.1214/ejp.v15-770
• Feng, C., Li, L., & Shen, J. (2010). Some Inequalities in Functional Analysis, Combinatorics, and Probability Theory. Electronic Journal of Combinatorics, 17(1), https://doi.org/10.37236/330
• Feng, C., Li, L., & Shen, J. (2009). On the Borel–Cantelli lemma and its generalization. Comptes Rendus Mathématique, 347(21-22), https://doi.org/10.1016/j.crma.2009.09.011
• Feng, C., & Zhao, H. (2008). Rough path integral of local time. Comptes Rendus Mathématique, 346(7-8), https://doi.org/10.1016/j.crma.2008.02.015
• Feng, C., & Zhao, H. (2007). A Generalized Ito's Formula in Two-Dimensions and Stochastic Lebesgue-Stieltjes Integrals. Electronic Journal of Probability, 12, https://doi.org/10.1214/ejp.v12-468
• Feng, C., & Zhao, H. (2006). Two-parameter p, q-variation Paths and Integrations of Local Times. Potential Analysis, 25(2), https://doi.org/10.1007/s11118-006-9024-2