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1. Full name: Tran Manh Cuong
2. Sex: Male
3. Date of birth: 21/12/1977
4. Place of birth: Ha Nam
5. Admission decision number 150/SĐH, dated July 6th, 2005.
6. Changes in academic process:
Decision number 1159/QĐ-SĐH, dated 30 June, 2008 of the rector of Hanoi University of Scicence to extend the education process.
Decision number 3458/QĐ-SĐH, dated 09 Oct., 2009 of President of Vietnam National University, Hanoi to pause the education process.
Decision number 27/ĐT-TS of the Dean of Graduate Department, VNU to allow the Ph.D student to continue the education process.
7. Official thesis title:
Extending random operators on separable Banach space
8. Major: Theory of Probability and Statistics
9. Code: 62 46 15 01
10. Supervisor:
1st: Prof.Dr.Sci. Dang Hung Thang – Hanoi University of Science,
2nd: Ass.Prof.Dr. Phan Viet Thu – Hanoi University of Science.
11. Summary of the new findings of the thesis:
- Give some sufficient conditions for a random operator admitting series expansion.
- Extending a linear random operator in case X is a Banach space with Schauder basis: Give some sufficient conditions for an X-valued random variable u belonging to the domain of the extended random operator as well as a necessary and sufficient condition for extending a linear random operator to the space of all X-valued r.v's. In addition, the above problem is considered in special case when the images of Schauder basis by the random operator are independent.
- Two methods of extending random operators are proposed: Extending by sequences and Extending by random series. In each method we give some sufficient conditions for an E-valued r.v. u in the domain of the extended random operators. In some cases, we also show the necessary and sufficient condition for extending a random operator to the whole space of all E-valued random variables.
12. Practical applicability:
13. Further research directions:
- Integral representation of a random operator.
- Find the necessary and sufficient conditions for extending by random series a random operator on the space of all E-valued random variables in the general case.
- Find other methods to extend random operators and their relationship.
14. Thesis-related publications:
[1] Dang Hung Thang and Tran Manh Cuong, A method of extending random operators, Acta Mathematica Vietnamica, 34(2009), 201-212.
[2] Dang Hung Thang and Tran Manh Cuong, Some procedures for extending random operators, Random operators and Stochastic equations, 17(2009), 359-380.
[3] Dang Hung Thang and Tran Manh Cuong, Series representation of random mappings and their extension, VNU Journal of Science, Mathematics-Physics, 25(2009) 237-248.
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