邵井海 教授
应用数学中心教师 主 页：
电 话：
邮 箱： shaojh@tju.edu.cn

研究方向：

随机分析、泛函不等式、随机（泛函）微分方程、带切换随机过程、金融风险估计

教育经历：

1996.7-2000.07　北京师范大学　概率论与数理统计 本科/学士

2000.7-2003.07　北京师范大学　概率论与数理统计 研究生/硕士

2003.09-2006.01　北京师范大学　概率论与数理统计 研究生/博士

2003.09-2006.09　法国第戎大学　随机分析 研究生/博士

代表性论文与著作：

[1] S. Fang, J. Shao, Transportation cost inequalities on path and loop groups, J. Functional Analysis 218(2005),293-317.

[2] 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.

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

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

[5] 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

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

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

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

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

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

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

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

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

[14] 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.

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

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

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

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

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

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

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

[22] 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.

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

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

[25] 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.

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

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

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

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