My research interests are Stochastic analysis on infinite dimensional spaces, Functional inequalities, Optimal transport map, Risk management and Regime-switching processes.

• Interested in the Functional inequalities, Stochastic analysis in infinite dimensional space, Optimal transport map, Estimation and Calculation of exit probability for stochastic processes, Regime-switching processes

• 2008, National Excellent Doctoral Dissertation of P.R. China, Ministry of Education
• 2007, Zhong Jiaqing Mathematics award, Chinese Mathematical Society

• 30. J. Shao, L.D. Wang, Variational formula for the stability of regime-switching diffusion processes, to appear SCIENCE CHINA Mathematics..2017
• 29. J. Shao, Ergodicity and first passage probability of regime-switching geometric Brownian motions, to appear in Chinese Annals of Mathematics, Series B. .2017
• 28. J. Shao, Stabilization of regime-switching process by feedback control based on discrete time observations, SIAM J. Control Optim. 55 (2017), no. 2, 724–740..2017
• 27. J. Bao, J. Shao, C. Yuan, Approximation of invariant measures for regime switching diffusions, Potential Anal. 44 (2016), no. 4, 707–727. .2017
• 26. J. Bao, J. Shao, Permanence and extinction of regime-switching predator-prey models, SIAM J. Math. Anal. 48 (2016), no. 1, 725–739. .2017
• 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. .2017
• 24. J. Shao, Criteria for transience and recurrence of regime-switching diffusion processes, Electron. J. Probab. 20 (2015), no. 63, 1–15..2017
• 23. H. Ji, J. Shao, First passage probabilities of one-dimensional diffusion process, Front. Math. China, 10(2015), 901–916..2017
• 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. .2017
• 21. J. Shao, Ergodicity of regime-switching diffusions in Wasserstein distances, Stoch. Proc. Appl. 125 (2015), pp. 739-758..2017
• 20. J. Shao, F. Xi, Stability and recurrence of regime-switching diffusion processes, SIAM J. Control Optim. 52(6), 3496-3516, 2014. .2017
• 19. J. Shao, Ergodicity of one-dimensional regime-switching diffusion processes, SCIENCE CHINA Mathematics 57(11), 2407-2414, 2014..2017
• 18. J. Shao, F. Xi, Strong ergodicity of the regime-switching diffusion processes. Stoch. Proc. Appl. 123 (2013), 3903-3918..2017
• 17. F. Xi, J. Shao, Successful Couplings for Diffusion Processes with State-Dependent Switching, SCIENCE CHINA Mathematics, 56(10), 2013, 2135-2144. .2017
• 16. J. Shao, Harnack inequalities and heat kernel estimates for SDEs with singular drifts, Bull. Sci. Math. 137(2013), 589-601. .2017
• 15. J. Shao, X. Wang, Estimates of exit probability for two correlated Brownian motions, Adv. Appl. Prob. 45(2013), 37-50 .2017
• 14. J. Shao, F.Y. Wang, C.G. Yuan, Harnack Inequalities for Stochastic (Functional) Differential Equations with Non-Lipschitzian Coefficients, Electron. J. Probab. 17 (2012), no. 100, 1–18. .2017
• 13. J. Shao, Measure-valued continuous curves and processes in total variation norm, J. Math. Anal. Appl. 392 (2012) 179-191..2017
• 12. S. Fang, J. Shao, Fokker-Planck equation with respect to heat measures on loop groups, Bull. Sci. math. 135 (2011) 775–794.2017
• 11. J. Shao, Transportation cost inequalities for Wasserstein diffusions, Bull. Sci. Math. 135 (2011), 383-394.2017
• 10. J. Shao, A new probability measure-valued stochastic process with Ferguson -Dirichlet process as reversible measure, Electron. J. Probab. 16 (2011) 271-292. .2017
• 9. J. Shao, From the heat measure to the pinned Wiener measure on loop groups， Bull. Sci. Math. 135 (2011) 601–612..2017
• 8. J. Shao, Harnack inequalities and HWI inequalities on infinite dimensional spaces, Acta Mathematica Sinica, English Series, 27 (2011), No. 6, 1195-1204..2017
• 7. S. Fang, J.Shao, T. Sturm, Wasserstein space over the Wiener space, Probab. Theory Related Fields, 146 (2010), 535-565.2017
• 6. J. Shao, Modified Logarithmic Sobolev Inequalities and Transportation Cost Inequalities in ℝn, Potential Analysis，31 ( 2009)，183-202.2017
• 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 .2017
• 4．S. Fang, J. Shao, Optimal transport maps for Monge-Kantorovich problem on loop groups, J. Funct. Anal. 248(2007), 225-257. .2017
• 3．J. Shao, Hamilton-Jacobi semigroups in infinite dimensional spaces, Bull. Sci. Math. 130 (2006), 720-738. .2017
• 2．S. Fang, J. Shao, Distance riemannienne, théorème de Rademacher et inégalité de transport sur le groupe des lacets, C.R. Acad. Sci. Paris. Ser. I 341(2005), 445-450. .2017
• 1．S. Fang, J. Shao, Transportation cost inequalities on path and loop groups, J. Functional Analysis 218 (2005), 293-317..2017