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Measure-valued processes and related topics -- An introduction.
Li, Z.H. (1991): Integral representations of continuous functions. Chinese Science Bulletin (Chinese Edition) 36, 2: 81-84 / (English Edition) 36, 12: 979-983.
Li, Z.H. (1992): Branching particle systems in random environments. Chinese Science Bulletin (Chinese Edition) 37, 17: 1541-1543.
Li, Z.H. (1992): A note on the multitype measure branching process. Advances in Applied Probability 24, 2: 496-498.
Li, Z.H. (1992): Measure-valued branching processes with immigration. Stochastic Processes and their Applications 43, 2: 249-264.
Li, Z.H. (1993): Branching particle systems with immigration. Rencontres Franco-Chinoises en Probabilites et Statistiques (Wuhan, 1990), Probability and Statistics 249-254, Edited by Badrikian, A. et al., World Scientific, Singapore.
Li, Z.H.; Li, Z.B.; Wang, Z.K. (1993): Asymptotic behavior of the measure-valued branching process with immigration. Science in China Series A (English Edition) 36, 7: 769-777.
Li, Z.H.; Shiga T. (1995): Measure-valued branching diffusions: immigrations, excursions and limit theorems. Journal of Mathematics of Kyoto University 35, 2: 233-274.
Li, Z.H. (1995/6): Convolution semigroups associated with measure-valued branching processes. Chinese Science Bulletin (Chinese Edition) 40, 22: 2018-2021 / (English Edition) 41, 4: 276-280.
Li, Z.H. (1996): Immigration structures associated with Dawson-Watanabe superprocesses. Stochastic Processes and their Applications 62, 1: 73-86.
Gorostiza, L.G.; Li, Z.H. (1998): Fluctuation limits of measure-valued immigration processes with small branching. Stochastic Models (Guanajuato, 1998), Sobretiro de Aportaciones Matematicas, Modelos Estocasticos 14, 261-268, Edited by Gonzalez-Barrios, J.M. and Gorostiza, L.G., Sociedad Matematica Mexicana.
Li, Z.H. (1998): Immigration processes associated with branching particle systems. Advances in Applied Probability 30, 3: 657-675.
Li, Z.H. (1998): Entrance laws for Dawson-Watanabe superprocesses with non-local branching. Acta Mathematica Scientia (English Edition) 18, 4: 449-456.
Li, Z.H. (1998): Absolute continuity of measure branching processes with mean field interactions. Chinese Journal of Applied Probability and Statistics 14, 3: 231-242.
Hong, W.M.; Li, Z.H. (1999): A central limit theorem for super Brownian motion with super Brownian immigration. Journal of Applied Probability 36, 4: 1218-1224.
Li, Z.H. (1999): Measure-valued immigration diffusions and generalized Ornstein-Uhlenbeck diffusions. Acta Mathematicae Applicatae Sinica (English Series) 15, 3: 310-320.
Li, Z.H. (1999): Some central limit theorems for super Brownian motions. Acta Mathematica Scientia (English Edition) 19, 2: 121-126.
Li, Z.H. (1999): A conditional law of super absorbing barrier Brownian motion. Chinese Journal of Applied Probability and Statistics 15, 1: 77-82.
Li, Z.H.; Pechersky, E.A. (1999): On large deviations in queuing systems. Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo 4, 2: 163-182.
Li, Z.H.; Shiga, T.; Yao, L.H. (1999): A reversibility problem for Fleming-Viot processes. Electronic Communications in Probability 4, 71-82.
Li, Z.H.; Wang, Z.K. (1999): Measure-valued branching process and immigration processes. Advances in Mathematics (China) 28, 2: 105-134.
Gorostiza, L.G.; Li, Z.H. (2000): High density fluctuations of immigration branching particle systems. Stochastic Models (Ottawa, Ontario, 1998), CMS Conference Proceedings, Series 26, 159-171, Edited by Gorostiza, L.G. and Ivanoff, B.G., AMS, Providence, RI.
Li, Z.H. (2000): Asymptotic behavior of continuous time and state branching processes. Journal of the Australian Mathematical Society (Series A) 68, 1: 68-84.
Li, Z.H. (2000): Ornstein-Uhlenbeck type processes and branching processes with immigration. Journal of Applied Probability 37, 3: 627-634.
Dawson, D.A.; Li, Z.H.; Wang, H. (2001): Superprocesses with dependent spatial motion and general branching densities. Electronic Journal of Probability 6, Paper No. 25, 1-33.
Hong, W.M.; Li, Z.H. (2001): Fluctuations of a super-Brownian motion with randomly controlled immigration. Statistics and Probability Letters 51, 3: 285-291.
Dawson, D.A.; Gorostiza, L.G.; Li, Z.H. (2002): Non-local branching superprocesses and some related models. Acta Applicandae Mathematicae 74, 1: 93-112.
Li, Z.H. (2002): Skew convolution semigroups and related immigration processes. Theory of Probability and its Applications 46, 2: 274-297. [tex file]
Dawson, D.A.; Li, Z.H. (2003): Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions. Probability Theory and Related Fields 127, 1: 37-61.
Dawson, D.A.; Li, Z.H.; Wang, H. (2003): A degenerate stochastic partial differential equation for the purely atomic superprocess with dependent spatial motion. Infinite Dimensional Analysis, Quantum Probability and Related Topics 6, 4: 597-607.
Li, Z.H.; Shiga, T.; Tomisaki, M. (2003): A conditional limit theorem for generalized diffusion processes. Journal of Mathematics of Kyoto University 43, 3: 567-583.
Dawson, D.A.; Li, Z.H. (2004): Non-differentiable skew convolution semigroups and related Ornstein-Uhlenbeck processes. Potential Analysis 20, 4: 285-302. [tex file]
Dawson, D.A.; Li, Z.H.; Schmuland, B.; Sun, W. (2004): Generalized Mehler semigroups and catalytic branching processes with immigration. Potential Analysis 21, 1: 75-97.
Dawson, D.A.; Li, Z.H.; Zhou, X.W. (2004): Superprocesses with coalescing Brownian spatial motion as large scale limits. Journal of Theoretical Probability 17, 3: 673-692.
Fu, Z.F.; Li, Z.H. (2004): Measure-valued diffusions and stochastic equations with Poisson process. Osaka Journal of Mathematics 41, 3: 727-744.
Li, Z.H.; Lu, G.H.; Wang, H. (2004): Immigration superprocesses with dependent spatial motion and non-critical branching. Chinese Annals of Mathematics Series A 25, 5: 627-636 / Chinese Journal of Contemporary Mathematics 25, 4: 405-416.
Li, Z.H.; Wang, H.; Xiong, J. (2004): A degenerate stochastic partial differential equation for superprocesses with singular interaction. Probability Theory and Related Fields 130, 1: 1-17.
Li, Z.H.; Wang, Z.K. (2004): Generalized Mehler semigroups and Ornstein-Uhlenbeck processes arising from superprocesses over the real line. Infinite Dimensional Analysis, Quantum Probability and Related Topics 7, 4: 591-605.
Hong, W.M.; Li, Z.H. (2005): Large and moderate deviations for occupation times of immigration superprocesses. Infinite Dimensional Analysis, Quantum Probability and Related Topics 8, 4: 593-603.
Li, Z.H.; Wang, H.; Xiong, J. (2005): Conditional log-Laplace functionals of immigration superprocesses with dependent spatial motion. Acta Applicandae Mathematicae 88, 2: 143-175.
Dawson, D.A.; Li, Z.H. (2006): Skew convolution semigroups and affine Markov processes. The Annals of Probability 34, 3: 1103-1142. [tex file]
Li, Z.H. (2006): A limit theorem for discrete Galton-Watson branching processes with immigration. Journal of Applied Probability 43, 1: 289-295.
Li, Z.H. (2006): Branching processes with immigration and related topics. Frontiers of Mathematics in China, Selected Publications from Chinese Universities 1, 1: 73-97.
Li, Z.H.; Zhang, M. (2006): Fluctuation limit theorems of immigration superprocesses with small branching. Statistics and Probability Letters 76, 4: 401-411.
Li, Z.H.; Xiong, J. (2007): Continuous local time of a purely atomic immigration superprocess with dependent spatial motion. Stochastic Analysis and Applications 25, 6: 1273-1296.
Li, Z.H.; Ma, C.H. (2008): Catalytic discrete state branching models and related limit theorems. Journal of Theoretical Probability 21, 4: 936-965.
Li, Z.H.; Wang, H.; Xiong, J. (2008): Conditional entrance laws for superprocesses with dependent spatial motion. Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, 2: 259-278.
Li, Z.H.; Zhou, X.W. (2008): Distributions and propagations of superprocesses with general branching mechanisms. Communications in Stochastic Analysis 2, 3: 469-477.
Fu, Z.F.; Li, Z.H. (2010): Stochastic equations of non-negative processes with jumps. Stochastic Processes and their Applications 120, 3: 306-330. [corrections]
Li, Z.H.; Xiong, J.; Zhang, M. (2010): Ergodic theory for a superprocess over a stochastic flow. Stochastic Processes and their Applications 120, 8: 1563-1588.
Li, Z.H.; Mytnik, L. (2011): Strong solutions for stochastic differential equations with jumps. Annales de l'Institut Henri Poincare: Probabilites et Statistiques 47, 4: 1055-1067.
Dawson, D.A.; Li, Z.H. (2012): Stochastic equations, flows and measure-valued processes. The Annals of Probability 40, 2: 813-857.
Li, Z.H.; Pu, F. (2012): Strong solutions of jump-type stochastic equations. Electronic Communications in Probability 17, 33: 1-13.
Li, Z.H.; Wang, H.; Xiong, J.; Zhou, X.W. (2012): Joint continuity for the solutions to a class of nonlinear SPDEs. Probability Theory and Related Fields 153, 3/4: 441-469.
Barczy, M.; Doring, L.; Li, Z.H.; Pap, G. (2013): On parameter estimation for critical affine processes. Electronic Journal of Statistics 7, 647-696.
He, H.; Li, Z.H.; Zhou, X.W. (2013): An integral test on time dependent local extinction for super-coalescing Brownian motion with Lebesgue initial measure. Journal of Theoretical Probability 26, 1: 31-45.
Li, Z.H.; Liu, H.L.; Xiong, J.; Zhou, X.W. (2013): The reversibility and an SPDE for the generalized Fleming-Viot processes with mutation. Stochastic Processes and their Applications. 123, 12: 4129-4155.
Barczy, M.; Doring, L.; Li, Z.H.; Pap, G. (2014): Stationarity and ergodicity for an affine two factor model. Advances in Applied Probability 46, 3: 878-898.
Barczy, M.; Doring, L.; Li, Z.H.; Pap, G. (2014): Parameter estimation for a subcritical affine two factor model. Journal of Statistical Planning and Inference 151-152, 37-59.
He, H.; Li, Z.H.; Yang, X. (2014): Stochastic equations of super-Levy process with general branching mechanism. Stochastic Processes and their Applications 124, 4: 1519-1565.
Li, Z.H. (2014): Path-valued branching processes and nonlocal branching superprocesses. The Annals of Probability 42, 1: 41-79.
Barczy, M.; Li, Z.H.; Pap, G. (2015): Yamada-Watanabe results for stochastic differential equations with jumps. International Journal of Stochastic Analysis 2015, Article ID 460472, 23 pages.
Barczy, M.; Li, Z.H.; Pap, G. (2015): Stochastic differential equation with jumps for multi-type continuous state and continuous time branching processes with immigration. Latin American Journal of Probability and Mathematical Statistics 12, 1: 129-169.
He, H.; Li, Z.H.; Zhou, X.W. (2015): Branching particle systems in spectrally one-sided Levy processes. Frontiers of Mathematics in China, Selected Publications from Chinese Universities 10, 4: 875-900.
Li, Z.H.; Ma, C.H. (2015): Asymptotic properties of estimators in a stable Cox-Ingersoll-Ross model. Stochastic Processes and their Applications 125, 8: 3196-3233.
Barczy, M.; Li, Z.H.; Pap, G. (2016): Moment formulas for multi-type continuous state and continuous time branching processes with immigration. Journal of Theoretical Probability 29, 3: 958-995.
He, X.; Li, Z.H. (2016): Distributions of jumps in a continuous-state branching process with immigration. Journal of Applied Probability 53, 4: 1166-1177.
Li, Z.H.; Xu, W. (2018): Asymptotic results for exponential functionals of Levy processes. Stochastic Processes and their Applications 128, 1: 108-131.
He, H.; Li, Z.H.; Xu, W. (2018): Continuous-state branching processes in L\'{e}vy random environments. Journal of Theoretical Probability 31, 4: 1952-1974.
Fang, R.; Li, Z.H. (2019): A conditioned continuous-state branching process with applications. Statistics and Probability Letters 152, 43-49.
Li, Z.H. (2019): Sample paths of continuous-state branching processes with dependent immigration. Stochastic Models 35, 2: 167-196.
Li, Z.H.; Zhang, W. (2019): Continuous-state branching processes with dependent immigration. Science in China Series A (Chinese Edition) 49, 3: 415-432. (In Chinese.)
Ji, L.N.; Li, Z.H. (2020): Moments of continuous-state branching processes with or without immigration. Acta Mathematicae Applicatae Sinica (English Series) 36 (2020), 2: 1-13.
Li, Z.H.; Yang, X.; Zong, G.W. (2020): A class of super-Levy processes in random environment. Science in China Series A (Chinese Edition) 50, 1: 69-86. (In Chinese.)
Li, Z.H. (2019+): Ergodicities and exponential ergodicities of Dawson--Watanabe type processes. Theory of Probability and its Applications. To appear.
Li, Z.H.; Pardoux, E.; Wakolbinger, A. (2019+): The height process of a continuous state branching process with interaction. Journal of Theoretical Probability. To appear.
Fang, R.J.; Li, Z.H. (2022): Construction of continuous-state branching processes in varying environments. The Annals of Applied Probability 32, 5: 3645--3673.
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