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Jinghai Shao

Professor

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Email: shaojh@bnu.edu.cn

Research Interests
• Stochastic analysis

• Functional inequalities

• Stochastic (functional) differential equations

• Regime-switching stochastic processes

• Estimate and control for financial risk
Education
• 1996.7 -- 2000.7,B.S, Probaility and statistics, Beijing Normal University, China

• 2000.7 -- 2003.7,M.Sc.,Probaility and statistics, Beijing Normal University, China

• 2003.9 -- 2006.1, Ph.D. Probaility and statistics, Beijing Normal University, China

•2003.9 -- 2006.9, Ph.D.Stochastic analysis, University of Dijon, France
Publications
• S. Fang, J. Shao, Transportation cost inequalities on path and loop groups, J. Functional Analysis 218(2005),293-317.

• S. Fang, J. Shao, Distance riemannienne, théorème de Rademacher et inégalitéde transport sur le groupe des lacets, C.R.Acad.Sci.Paris. Ser. I 341(2005), 445-450.

• J. Shao, Hamilton-Jacobi semigroups in infinite dimensional spaces, Bull.Sci.Math.130(2006), 720-738.

• S. Fang, J. Shao, Optimal transport maps for Monge-Kantorovich problem on loop groups, J. Funct. Anal. 248(2007), 225-257.

• J. Shao, Y.H. Mao, Estimation of the Dirichlet eigenvalues of birth-death process on trees, ACTA Math. Sinica. Chinese series, 50( 2007), 507-516

• J. Shao,Modified Logarithmic Sobolev Inequalities and Transportation Cost Inequalities in ℝn, Potential Analysis,31 ( 2009),183-202

• S. Fang, J.Shao, T. Sturm, Wasserstein space over the Wiener space, Probab. Theory Related Fields,146 (2010),535-565.

• J. Shao, Harnack inequalities and HWI inequalities on infinite dimensional spaces, Acta Mathematica Sinica, English Series, 27 (2011), No. 6, 1195-1204.

• J. Shao, From the heat measure to the pinned Wiener measure on loop groups,Bull. Sci. Math. 135 (2011) 601-612.

• J. Shao, A new probability measure-valued stochastic process with Ferguson-Dirichlet process as reversible measure, Electron. J. Probab.16 (2011) 271-292.

• J. Shao, Transportation cost inequalities for Wasserstein diffusions, Bull. Sci. Math.135 (2011), 383-394

• S. Fang, J.Shao, Fokker-Planck equation with respect to heat measures on loop groups, Bull. Sci. math. 135 (2011) 775-794

• J. Shao, Measure-valued continuous curves and processes in total variation norm, J. Math. Anal. Appl. 392 (2012) 179-191.

• J. Shao, F.Y. Wang, C.G. Yuan, Harnack Inequalities for Stochastic(Functional) Differential Equations withNon-Lipschitzian Coefficients, Electron. J. Probab.17 (2012), no. 100, 1-18.

• J. Shao, X. Wang, Estimates of exit probability for two correlated Brownian motions, Adv. Appl. Prob. 45(2013), 37-50

• J. Shao, Harnack inequalities and heat kernel estimates forSDEs with singular drifts, Bull. Sci. Math.137(2013), 589-601.

• F. Xi, J. Shao,Successful Couplings for Diffusion Processes with State-Dependent Switching, SCIENCE CHINA Mathematics,56(10), 2013, 2135-2144.

• J. Shao, F. Xi, Strong ergodicity of the regime-switching diffusion processes. Stoch. Proc. Appl. 123 (2013), 3903-3918.

• J. Shao, Ergodicity of one-dimensional regime-switching diffusion processes, SCIENCE CHINA Mathematics 57(11), 2407-2414, 2014

• J. Shao, F. Xi, Stability and recurrence of regime-switching diffusion processes, SIAM J. Control Optim. 52(6), 3496-3516, 2014.

• J. Shao, Ergodicity of regime-switching diffusions in Wasserstein distances, Stoch. Proc. Appl. 125 (2015),pp. 739-758

• J. Shao, C.G. Yuan, Transportation-cost inequalities for diffusions with jumps and its application to regime-switching processes.J. Math. Anal. Appl.425 (2015), 632-654.

• H. Ji, J. Shao, First passage probabilities of one-dimensional diffusion process, Front. Math. China, 10(2015), 901-916.

• J. Shao, Criteria for transience and recurrence of regime-switching diffusionprocesses, Electron. J. Probab.20 (2015), no. 63, 1-15.

• J. Shao, Strong solutions and strong Feller properties for regime-switching diffusion processes in an infinite state space, SIAM J. Control Optim. 53 (2015), no. 4, 2462-2479.

• J. Bao, J. Shao, Permanence and extinction of regime-switching predator-prey models, SIAM J. Math. Anal. 48 (2016), no. 1, 725-739.

• J. Bao,J. Shao, C.Yuan,Approximation of invariant measures for regime switching diffusions, Potential Anal. 44 (2016), no. 4, 707-727.

• J. Shao, Ergodicity and first passage probability of regime-switching geometric Brownian motions, to appear in Chinese Annals of Mathematics, Series B.

• J. Shao, Stabilization of regime-switching process by feedback control based on discrete time observations, to appear inSIAM J. Control Optim.


Center for Applied Mathematics, Tianjin University, No.92 Weijin Road, Tianjin 300072, P. R. China