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Xiaowen Zhou, PhD

  • Full Professor, Mathematics and Statistics

Research areas: Stochastic processes and applications

Contact information

Biography

Education

Ph.D.:  University of California (Berkeley), U.S.A. 1999

Research interests

Measure-Valued Stochastic Processes, Levy Processes, Mathematical Population Genetics

Teaching activities

Winter 2023

STAT250: Statistics 
MAST 679V: Levy Processes

Publications

Some recent preprints

Li, P.-S., Li, Z., Wang, J. and Zhou, X. Exponential ergodicity of  branching processes with immigration and competition. Accepted. Annales de L'Institut Henri Poincare (B) Probabilites et Statistiques.

Li, P.-S., Wang, J. and Zhou X. Quasi-stationary distribution for continuous-state branching processes with competition. Accepted. Stochastic Processes and their Applications.

Li B., Foucart, C. and Zhou, X. Behaviors near explosion of nonlinear CSBPs with regularly varying branching mechanism.


Some recent papers

Li, Z., Liu, H., Xiong, J. and Zhou, X. (2013). The irreversibility and an SPDE for the generalized Fleming-Viot processes with mutation. Stochastic Processes and their Applications 123, 4129-4155. 

Li, B. and Zhou X. (2013). The joint Laplace transforms for diffusion occupation times. Advances in Applied Probability 45,1049-1067. 

Zhou, X. (2014) On criteria of  disconnectedness for $\Lambda$-Fleming-Viot support. Electronic Communications in Probability 19 no 53, 1-16. 

Loeffen R.,  Renaud, J.-F. and Zhou, X. (2014). Occupation times of intervals until first passage times for spectrally negative Levy processes. Stochastic Processes and their Applications 124, 1408-1435. 

Li, Y. and Zhou, X. (2014). On pre-exit joint occupation times for spectrally negative Levy processes. Statistics and Probability Letters 94, 48-55. 

Liu, H. and Zhou X. (2015). Some support properties  for a class of $\Lambda$-Fleming-Viot processes. Annales de L'Institut Henri Poincare (B) Probabilites et Statistiques, 1076-1101. 

Albrecher, H., Ivanovs, J. and Zhou, X. (2016). Exit identities for a Levy processes observed at Poisson arrival times. Bernoulli 22, 1364-1382.   

Wang, L., Yang, X. and Zhou, X. (2017). A distribution-function-valued SPDE and its applications. Journal of Differential Equations 262, 1085-1118. 

Yang, X. and Zhou, X. (2017). The pathwise uniqueness of solution to a SPDE driven by $\alpha$-stable noise with Holder continuous coefficient. Electronic Journal of Probability 22, no. 4, 1-48. 

Avram, F.,  Vu, N. L. and Zhou, X. (2017). On taxed spectrally negative Levy processes with draw-down stopping. Insurance, Mathematics and Economics 76, 69-74. 

Li, B. and Zhou, X. (2018) On  weighted occupation times for refracted spectrally negative Levy processes. Journal of Mathematical Analysis and Applications 466, 215-237. 

Wang, W. and Zhou, X. (2018).  General draw-down based de Finetti optimization for spectrally negative Levy risk processes. Journal of Applied Probability 55, 1-30. 

Li, P. S., Yang, X. and Zhou, X. (2019). A general continuous-state nonlinear branching process. Annals of Applied Probability 29, 2523-2555.

Xiong, J., Zheng, J., and  Zhou X. (2019). Unique strong solutions of Levy processes driven stochastic differential equations with discontinuous coefficients. Stochastics. 91, 592-612.

Li, B., Vu, N. L.  and Zhou, X. (2019). Exit problems for general draw-down times of spectrally negative Levy processes. Journal of Applied Probability 56, 441-457. 

Wang, W.  and Zhou, X. (2020). Draw-down Parisian ruin for spectrally negative Levy process. Advances in Applied Probability 52, 1164-1196.  

Li, B. and Zhou, X. (2020). Local times for spectrally negative Levy processes. Potential Analysis 52, 689-711.

Wang, W. and Zhou, X. (2021)A draw-down reflected spectrally negative Levy process. Journal of Theoretical Probability 34, 283-306.

Foucart, C. Li, P.-S. and Zhou, X. (2021). Time-changed spectrally positive Levy processes started from infinity. Bernoulli 27, 1291-1318.

Li B. and Zhou X. (2021). On the explosion of a class of continuous-state
nonlinear branching processes. Electronic Journal of Probability 26, no.148, 1-25.

Ma, S., Yang, X. and Zhou, X. (2021). A note on boundary behaviors of a class of continuous-state nonlinear branching processes. Electronic Communication in Probability 26, no. 6, 1-10.

Li, J., Tang, Y. and Zhou, X. (2022). Extinguishing behaviors for continuous-state nonlinear branching processes. Journal of Mathematical Analysis and Applications 514, 126326. 

Li, S. and Zhou, X. (2022). The Parisian and ultimate drawdowns of Levy insurance models. Insurance, Mathematics and Economics 107, 140-160.

Ren, Y., Yang, X., Xiong, J. and Zhou, X. (2022). On the extinction-extinguishing dichotomy for a stochastic Lotka-Volterra type population dynamical system. Stochastic Processes and their Applications 150, 50-90.

Foucart, C. and Zhou, X. (2022).  On the  explosion of the number of fragments in the simple exchangeable fragmentation-coalescence processes. Annales de L'Institut Henri Poincare (B) Probabilites et Statistiques 58, 1182-1207.

Surya, B., Wang, W., Zhao, X. and Zhou, X. (2023). Parisian excursion with capital injection for draw-down reflected Levy insurance risk process. Scandinavia Actuarial Journal 2023, 97-122.

Li, P.S. and Zhou, X. (2023). Integral Functionals for Spectrally Positive Levy Processes. Journal of Theoretical Probability 36, 297-314.

Foucart, C. and Zhou, X. (2023). On the boundary classification of $\Lambda$-Wright-Fisher processes with frequency-dependent selection.   Annales Henri Lebesgue 6, 493-539.

Hughes, H. and Zhou, X. (2023). Instantaneous support propagation for  $\Lambda$-Fleming-Viot processes. Stochastic Processes and their Applications 155, 535-560.

B. li and X. Zhou. (2024).  An excursion theoretic approach to Parisian ruin problem. \emph{Insurance, Mathematics and Economics 118, 44-58.

Ma, R. and Zhou, Z. (2024).  Explosion of continuous-state branching processes with competition in Levy  environment. Journal of Applied Probability 61, 68-81.

Wang, Y., Yan, C. and  Zhou, X. (2024). Comparison principle for a class of stochastic heat equations driven by $\alpha$-stable white noises. Bernoulli 30, 1375-1400.

Liu, H. and Zhou X. (2024). Exact modulus of continuities for  $\Lambda$-Fleming-Viot processes with Brownian spatial motion. Journal of Theoretical Probability 37, 1710-1744.


                       
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