General

Xiaoyu Hu, Ph.D

Professor

School of Mathematics Sciences, Graduate University of Chinese Academy of Sciences

19A Yuquan Road, Beijing 100049, P.R. China

Email: xyhu@gucas.ac.cn

Professor

School of Mathematics Sciences, Graduate University of Chinese Academy of Sciences

19A Yuquan Road, Beijing 100049, P.R. China

Email: xyhu@gucas.ac.cn

### Research Areas

Sample path properties and geometry properties of Stochastic processes

Markov process in random environment

Markov process in random environment

### Education

Department of mathematics, University of Virginia , Ph.D

### Publications

Selected Papers:

1. Gao Z.L. Hu X Y. The limit theory for a branching process with the iid random environment, Acta Mathematica Scientia 2011

2. Gao Z.L. Hu X Y. The law of the iterated logarithm for random sums of a double random sequence, Journal of Gradute University of Chinese Academy of Sciences, 2011,28(4):424-430. (in Chinese).

3. Shi H.H. Hu X Y. Asymptotic properties of the sample paths of additive Levy processes, Sci China Ser A, 2011,41(4):353-364. (in Chinese).

4. Fang L. Hu X Y. Some limit theorems on branching random walks in random environments, Journal of Gradute University of Chinese Academy of Sciences, 2011,28(3):288-297. (in Chinese).

5. Shen D, Hu X Y. The multifractal structure of the product of two stable occupation measures. Statistics and Probability Letters 81 (2011) 478–488.

6. Xiaoyu Hu, Jason Miller and Yuval Peres. Thick points of the Gaussian free field. The Annals of Probability, 2010, Vol. 38, No. 2, 896–926.

7. Hu D H, Hu X Y. The branching chain with drift in space-time random environment (I): Model, Markov property, Moments. Acta Mathematica Scientia, 2010(5): 1669-1678

8. Hu D H, Hu X Y. On markov chains in space time random environments. Acta Mathematica Scientia 2009,29B(1):1–10.

9. Kong L T, Hu X Y. Multifractal structure of the product measure of two independent general subordinators’ occupation measures. Sci China Ser A, 2009, 52(8): 1785–1795.

10. Kong L T, Shen D, Hu X Y. The fractal structures of the exceptional sets of Levy processes. Sci China Ser A, 2009, 52(7): 1459–1466.

11. Kong L T, Hu X Y. Multifractal analysis of the product measure of two general subordinators. Sci China Ser A, 2009, 39(6):689-699.

12. Hu X Y. The law of the iterated logarithm for the Gaussian free field. Statistics and Probability Letters 78 (2008) 3023-3028.

13. Hu D H, Hu X Y. The construction of denumerable q-processes in random environments satisfying (F) or (B). Acta Mathematica Scientia 2008,28B(4):975–988.

14. Hu D H, Hu X Y. The construction of denumerable q-processes in random environments-The existence and uniqueness. Acta Mathematica Scientia 2008,28B(2):225–235.

15. Xiaoyu Hu, S.James Taylor. Multifractal structure of a general subordinator. Stochastic Processes and their Applications, Volume 88, Issue 2, August 2000, Pages 245-258.

16. Xiaoyu Hu. The fractal properties of the random cantor sets and percolation processes. Acta Mathematic Applicate Sinica 2000,23(2): 270-274. (in Chinese).

17. Xiaoyu Hu. Multifractal analysis of the occupation measures of a kind of stochastic processes. Stochastic Processes and their Applications, Volume 80, Issue 2, 1 April 1999, Pages 249-269.

18. Xiaoyu Hu. The probability properties of random cantor sets. Acta Mathematicae Applicate Sinica, 1999,22(4): 599-606. (in Chinese).

19. Xiaoyu Hu, S.James Taylor. The multifractal structure of stable occupation measure. Stochastic Processes and their Applications, Volume 66, Issue 2, 28 March 1997, Pages 283-299.

20. Hu D H, Hu X Y. The dimension of the zero set for a recurrent random walk. Science in China(Series A), 1995,1(4): 435-440. (in Chinese).

21. Xiaoyu Hu. Some fractal sets determined by stable processes. Probab. Theory Related Fields 100, 1994, 205–225.

22. Xiaoyu Hu, S.James Taylor.Fractal properties of products and projections of measures in Rd.Math. Proc. Camb. Phil. Soc. 1994,(115) 527-544.

23. Xiaoyu Hu. The Packing measure of rearrangements of Cantor sets. Science in China(Series A), 1994,24(9): 926-932. (in Chinese).

24. Xiaoyu Hu. The Hausdorff measure of rearrangements of Cantor sets. Science in China(Series A), 1994,24(8): 815-826. (in Chinese).

25. Xiaoyu Hu. Fractal properties and the Hausdorff measure of the random Cantor sets and a subordinator. Chinese Science Bulletin, 1994,39(15): 1345-1348. (in Chinese).

26. Hu D H, Hu X Y. Discrete fractal of a recurrent random walk. Chinese Science Bulletin, 1994,39(15): 1438-1438. (in Chinese).

27. Hu X Y. The convergence and Riesz decomposition of MIL valued in Banach space in a directed set. Acta Mathematica Scientia. 1990,10(2): 174-180. (in Chinese).

1. Gao Z.L. Hu X Y. The limit theory for a branching process with the iid random environment, Acta Mathematica Scientia 2011

2. Gao Z.L. Hu X Y. The law of the iterated logarithm for random sums of a double random sequence, Journal of Gradute University of Chinese Academy of Sciences, 2011,28(4):424-430. (in Chinese).

3. Shi H.H. Hu X Y. Asymptotic properties of the sample paths of additive Levy processes, Sci China Ser A, 2011,41(4):353-364. (in Chinese).

4. Fang L. Hu X Y. Some limit theorems on branching random walks in random environments, Journal of Gradute University of Chinese Academy of Sciences, 2011,28(3):288-297. (in Chinese).

5. Shen D, Hu X Y. The multifractal structure of the product of two stable occupation measures. Statistics and Probability Letters 81 (2011) 478–488.

6. Xiaoyu Hu, Jason Miller and Yuval Peres. Thick points of the Gaussian free field. The Annals of Probability, 2010, Vol. 38, No. 2, 896–926.

7. Hu D H, Hu X Y. The branching chain with drift in space-time random environment (I): Model, Markov property, Moments. Acta Mathematica Scientia, 2010(5): 1669-1678

8. Hu D H, Hu X Y. On markov chains in space time random environments. Acta Mathematica Scientia 2009,29B(1):1–10.

9. Kong L T, Hu X Y. Multifractal structure of the product measure of two independent general subordinators’ occupation measures. Sci China Ser A, 2009, 52(8): 1785–1795.

10. Kong L T, Shen D, Hu X Y. The fractal structures of the exceptional sets of Levy processes. Sci China Ser A, 2009, 52(7): 1459–1466.

11. Kong L T, Hu X Y. Multifractal analysis of the product measure of two general subordinators. Sci China Ser A, 2009, 39(6):689-699.

12. Hu X Y. The law of the iterated logarithm for the Gaussian free field. Statistics and Probability Letters 78 (2008) 3023-3028.

13. Hu D H, Hu X Y. The construction of denumerable q-processes in random environments satisfying (F) or (B). Acta Mathematica Scientia 2008,28B(4):975–988.

14. Hu D H, Hu X Y. The construction of denumerable q-processes in random environments-The existence and uniqueness. Acta Mathematica Scientia 2008,28B(2):225–235.

15. Xiaoyu Hu, S.James Taylor. Multifractal structure of a general subordinator. Stochastic Processes and their Applications, Volume 88, Issue 2, August 2000, Pages 245-258.

16. Xiaoyu Hu. The fractal properties of the random cantor sets and percolation processes. Acta Mathematic Applicate Sinica 2000,23(2): 270-274. (in Chinese).

17. Xiaoyu Hu. Multifractal analysis of the occupation measures of a kind of stochastic processes. Stochastic Processes and their Applications, Volume 80, Issue 2, 1 April 1999, Pages 249-269.

18. Xiaoyu Hu. The probability properties of random cantor sets. Acta Mathematicae Applicate Sinica, 1999,22(4): 599-606. (in Chinese).

19. Xiaoyu Hu, S.James Taylor. The multifractal structure of stable occupation measure. Stochastic Processes and their Applications, Volume 66, Issue 2, 28 March 1997, Pages 283-299.

20. Hu D H, Hu X Y. The dimension of the zero set for a recurrent random walk. Science in China(Series A), 1995,1(4): 435-440. (in Chinese).

21. Xiaoyu Hu. Some fractal sets determined by stable processes. Probab. Theory Related Fields 100, 1994, 205–225.

22. Xiaoyu Hu, S.James Taylor.Fractal properties of products and projections of measures in Rd.Math. Proc. Camb. Phil. Soc. 1994,(115) 527-544.

23. Xiaoyu Hu. The Packing measure of rearrangements of Cantor sets. Science in China(Series A), 1994,24(9): 926-932. (in Chinese).

24. Xiaoyu Hu. The Hausdorff measure of rearrangements of Cantor sets. Science in China(Series A), 1994,24(8): 815-826. (in Chinese).

25. Xiaoyu Hu. Fractal properties and the Hausdorff measure of the random Cantor sets and a subordinator. Chinese Science Bulletin, 1994,39(15): 1345-1348. (in Chinese).

26. Hu D H, Hu X Y. Discrete fractal of a recurrent random walk. Chinese Science Bulletin, 1994,39(15): 1438-1438. (in Chinese).

27. Hu X Y. The convergence and Riesz decomposition of MIL valued in Banach space in a directed set. Acta Mathematica Scientia. 1990,10(2): 174-180. (in Chinese).