Tiexin Guo

Professor

tiexinguo@csu.edu.cn

Research

Research Area:

Mathematics

Research Interests:

1.Functional Analysis (Banach Space Theory,Random Metric Theory); 2.Mathematical Finance (Dynamic Risk Measures)

 

Contact Information

School of Mathematics and Statistics

Central South University

Changsha, Hunan, 410083

P.R.China

tiexinguo@csu.edu.cn

Education

Ph.D: 1992,  Xi’an Jiaotong University,China

M.Sc: 1989,  Xi’an Jiaotong University,China

B.S:  1986,  Xi’an JiaotongUniversity, China

 

Academic Positions:

Professor: School of Mathematics andStatistics, Central South University, 2012-present;

Professor: School of Mathematics and SystemSciences, Beihang University, 2006.8-2011;

Professor: School of Mathematical Sciences,Xiamen University, 1999.12-2006.8 (He became Advisor of Doctoral students from2002)

Senior visiting scholar: Department ofMathematics, MIT, 2001.9-2002.3

Associate Professor: School of MathematicalSciences, Xiamen University, 1994.10-1999.11

Post Dr. Mathematics, Sichuan University, 1992.7-1994.7

Teaching

Mathematical Analysis, Functional Analysis,Topology, Measure Theory, Stochastic Analysis, Mathematical Finance.

 

Publications

Selected Publications (listed back in time):

 

1. TieXin Guo, ShiEn Zhao, XiaoLin Zeng. Randomconvex analysis(I): Separation and Fenchel-Moreau duality in random locallyconvex modules (in Chinese). Sci.Sin.Math., 2015. (See also, [Guo Tiexin, ZhaoShien, Zeng Xiaolin. Random convex analysis(I): Separation and Fenchel-Moreauduality in random locally convex modules. 2015, arXiv: 1503.08695.])

2. TieXin Guo, ShiEn Zhao, XiaoLin Zeng. Random convex analysis(II):continuity and

subdifferentiability theorems in L^0-pre-barreled random locallyconvex modules(in Chinese). Sci.Sin.Math., 2015, 45(5): 647-662. (See also, [GuoTiexin, Zhao Shien, Zeng Xiaolin. Random convex analysis(II): continuity and subdifferentiabilitytheorems in L^0-pre-barreled random locally convex modules. 2015, arXiv: 1503.08637.])

3. TieXin Guo, ShiEn Zhao, XiaoLin Zeng .The relations among thethree kinds of

conditional risk measures. Sci. China Math., 2014, 57: 1753--1764.

4. MingZhi Wu, TieXin Guo. A counterexampleshows that a locally L^0-convex topology is not necessarily induced by a familyof L^0-seminorms. 2015, arXiv: 1501.04400.

5. TieXin Guo, ShiEn Zhao, XiaoLin Zeng. On random convexanalysis--the analytic foundation for conditional convex risk measures. 2012,arXiv: 1210.1848.
6. ShiEn Zhao,TieXin Guo. The random subreflexivity of complete random normedmodules , International Journal of Mathematics
2012233):12500471-14.
7. TieXin Guo, ShiEn Zhao. On the random conjugate spaces of a random locallyconvex module, Acta Math.Sinica
2012284):687-696.
8. TieXin Guo, XiaoLin Zeng. An L0- valued function’s intermediate valuetheorem and its applications to random uniform convexity, Acta Math. Sinica(English Ser.), 2012, 28
5):909-924.
9. TieXin Guo, Xia Zhang. Stone’s representation theorem of a group of randomunitary

operators on complete complex random innerproduct modules (in Chinese), Sci. Sin. Math., 2012, 42(3): 181-202.
10. TieXin Guo. Recent progress in random metric theory and its applications toconditional risk measures, Sci. China Ser. A , 2011, 54(4): 633-660.

11. TieXin Guo, Guang Shi. The algebraicstructure of finitely generated L0- modules and the Helly theorem in randomnormed modules, J. Math. Anal. Appl., 2011, 381: 833-842.
12. TieXin Guo,Yujie Yang. Ekeland’s variational principle for an L0-valuedfunction on a complete random metric space,J.Math. Anal. Appl., 2011,389:1-14.
13. TieXin Guo. Relations between some basic results derived from two kinds oftopologies for a random locally convex module, Journal of Functional Analysis,2010, 258:3024-3047.
14.TieXin Guo, Xiaolin Zeng. Random strict convexity and random uniformconvexity in random normed modules, Nonlinear Analysis Series A: Theory,Methods and Applications, 2010, 73:1239-1263.
15. TieXin Guo, Haixia Xiao, Xinxiang Chen. A basic strict separation theoremin random locally convex modules, Nonlinear Analysis Series A: Theory, Methodsand Applications, 2009, 71:3794-3804.

16. TieXin Guo. Xinxiang Chen, Randomduality, Sci. China Ser. A, 2009, 52:2084-2098.
17. TieXin Guo. The relation of Banach-Alaoglu theorem andBanach-Bourbaki-Kakutani-Smulian theorem in complete random normed modules tostratification structure, Sci. China Ser. A, 2008, 51:1651-1663.
18. TieXin Guo. Several applications of the theory of random conjugate spacesto measurability problems, Sci. China Ser. A, 2007, 50:737-747.
19.TieXin Guo, ShaoBin Li. The James Theorem in complete random normed modules,J. Math. Anal. Appl., 2005, 308 : 257-265.
20. TieXin Guo, LinHu Zhu. A characterization of continuous modulehomomorphisms on random seminormed modules and its applications, Acta MathematicaSinica, English Series, 2003, 19(1):201-208.
21. TieXin Guo, ShengLan Peng. A characterization for an L(μ
K)-topological module to admitenough canonical module homomorphisms, J. Math. Anal. Appl., 2001,263:580-599.
22. TieXin Guo. Representation theorems of the dual of Lebesgue-Bochnerfunction spaces, Sci. China Ser. A, 2000, 43: 234-243.

23. TieXin Guo, ZhaoYong You. A note onpointwise best approximation, J. of Approximation Theory, 1998,93(2):344-347.
24. TieXin Guo. The Radon-Nikodym property of conjugate spaces and the w-starequivalence theorem for w-star measurable functions, Sci. China Ser. A, 1996,39:1034-1041.
25. TieXin Guo
ZhaoyongYou. Riesz’s representation theorem in complete random inner product modules,Chinese Ann. Math. Ser. A , 1996, 17: 361-364.
26. TieXin Guo. Extension theorems of continuous random linear operators onrandom domains, J. Math. Anal. Appl., 1995, 193(1):15-27.
27. TieXin Guo. A weak equivalence theorem of weak random elements in weaklycompactly generated Banach spaces and its applications, Chinese ScienceBulletin, 1995, 40(24):2212-2214.
28. ZhaoYong You, TieXin Guo. Pointwise best approximation in the space ofstrongly measurable functions with applications to best approximation in Lp(μ, X),J. of Approximation Theory, 1994, 78(3):314-320.

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