PAPERS in REFEREED JOURNALS/BOOK CHAPTERS

1. J. Song, J. Yao and W. Yuan: High-dimensional central limit theorems for eigenvalue distributions of generalized Wishart processes.  Submitted.

2. J. Song, X. Song and F. Xu: Fractional stochastic wave equation driven by a Gaussian noise rough in space. Submitted.

3. M. Choi, C. Lee and J. Song: Entropy flow and De Bruijn’s identity for a class of stochastic differential equations driven by fractional Brownian motion. Probability in the Engineering and Informational Sciences, 2019

4. J. Song, J. Yao and W. Yuan: High-dimensional limits of eigenvalue distributions for general Wishart process. Annals of Applied Probability (accepted)

5. R. M. Balan, L. Quer-Sardanyons and J. Song: H ̈older continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise. Acta Mathematica Scientia (Accepted).

6. R. M. Balan, L. Quer-Sardanyons and J. Song: Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise. Electronic Journal of Probability (accepted).

7. J. Song, X. Song and Q. Zhang: Nonlinear Feynman-Kac formulae for SPDEs with space-time noise. SIAM J. Math. Anal. 51 (2019), no. 2, 955-990.

8. J. Song, F. Xu and Q. Yu: Limit theorems for functionals for two independent Gaussian processes.Stochastic Processes and Their Applications (Accepted).

9. J. Song: SPDEs with colored Gaussian noise: a survey. Commun. Math. Stat. 6 (2018), no. 4, 481-492.

10. R. M. Balan and J. Song: Second order Lyapunov exponents for parabolic and hyper- bolic Anderson models. Bernoulli (Accepted).

11. X. Chen, Y. Hu, J. Song and X. Song: Temporal asymptotics for fractional parabolic Anderson model. Electron. J. Probab. 23 (2018), No. 14, 39 pp.

12. R. Balan, J. Song: Hyperbolic Anderson Model with space-time homogeneous Gaussian noise. ALEA Lat. Am. J. Probab. Math. Stat. 14 (2017), no. 2, 799-849.

13. J. Song: On a class of stochastic partial differential equations. Stochastic Processes and Their Applications, 127 (2017), no. 1, 37-79.

14. G. Han and J. Song: Extensions of the I-MMSE Relation. IEEE Transactions on Information Theory, 62 (2016), no. 10, 5422-5445.

15. C. Lee and J. Song: On drift parameter estimation for reflected fractional Ornstein- Uhlenbeck processes. Stochastics 88 (2016), no. 5, 751-778.

16. X. Chen, Y. Hu, F. Xing and J. Song: Exponential asymptotics for time-space Hamil- tonians. Ann. Inst. Henri Poincar Probab. Stat. 51 (2015), no. 4, 1529-1561.

17. Y. Hu, C. Lee, M. Lee and J. Song: Parameter estimation for reflected Ornstein- Uhlenbeck processes with discrete observations, with Y. Hu, C. Lee and M. Lee. Statistical Inference for Stochastic Processes, 18 (2015), no. 3, 279-291.

18. Y. Hu, D. Nualart and J. Song: The 4/3-variation of the derivative of the self- intersection Brownian local time and related processes. J. Theoret. Probab., 27 (2014), no. 3, 789-825.

19. Y. Hu and J. song: Parameter estimation for fractional Ornstein-Uhlenbeck processes with discrete observations. Malliavin calculus and stochastic analysis, 427-442, Springer Proc. Math. Stat., 34, Springer, New York, 2013.

20. Y. Hu, D. Nualart and J. Song: A nonlinear stochastic heat equation: H ̈older con- tinuity and smoothness of the density of the solution. Stochastic Processes and their Applications, Vol 123, Issue 3, March 2013, Pages 1083-1103.

21. Y. Han, Y. Hu and J. Song: Maximum principle for controlled systems driven by fractional brownian motions. Appl. Math. Optim. 67 (2013), no. 2, 279-322.

22. J. Song: Asymptotic behavior of the solution of heat equation driven by fractional white noise. Statistics and Probability Letters 2012. 82 no. 3, 614-620.

23. Y. Hu, D. Ocone and J. Song: Some results on backward stochastic differential equa- tions driven by fractional Brownian motions. Stochastic analysis and applications to fi- nance, 225-242, Interdiscip. Math. Sci., 13, World Sci. Publ., Hackensack, NJ, 2012.

24. Y. Hu, D. Nualart and J. Song: Feynman-Kac formula for heat equation driven by a fractional white noise. The Annals of Probability 2011, Vol. 39, No. 1, 291-326.

25. Y. Hu, D. Nualart and J. Song: Fractional martingales and characterization of the fractional Brownian motion. The Annals of Probability 2009, Vol. 37, No. 6, 2404-2430.

26. Y. Hu, D. Nualart and J. Song: Integral representation of renormalized self-intersection local times. Journal of Functional Analysis 255, 2507-2532, 2008.

SELECTED CONFERENCE PRESENTATIONS

1. International Workshop on Probability, Uncertainty, and Quantitative Risk July 11-14, 2019, Shandong University, Weihai, China. Title: High-dimensional central limit theorems for eigenvalue distributions of generalized Wishart processes.

2. IMS China Meeting July 6-10, 2019 Dalian, China. Title: Fractional stochastic wave equation driven by a Gaussian noise rough in space.

3. Departmental Colloquium at City University of Hong Kong, November 28, 2017. Title: Temporal asymptotics for some Andreson models.

4. Hong Kong Probability Seminar, November 17, 2017. Title: Long-term asymptotics for (fractional) Anderson models.

5. SIAM Conference on Control and its Applications at Pittsburgh, July 12, 2017. Title: Some results on optimal stopping problems for one-dimensional regular diffusions.

6. Probability Seminar at Purdue University, March 28, 2017. Title: Temporal asymptotics for fractional parabolic Anderson model.

7. Conference on stochastic processes and applied probability, Jilin University, China, May 30 - June 03, 2016. Title: Temporal asymptotics for fractional parabolic Anderson model.

8. Workshop on Mathematical Finance and Financial Data Processing, Soochow University, China, April 28 - 29, 2016. Title: Temporal asymptotics for fractional parabolic Anderson model.

9. Conference on stochastic processes, stochastic analysis and related fields, Sichuan Uni- versity, China, April 14 - 15, 2016. Title: Hyperbolic Anderson Model with space-time homogeneous Gaussian noise.

10. Youth Probability Forum, Peking University, China, July 8, 2015. Title: Nonlinear Feynman-Kac formula for quasilinear stochastic partial differential equations.

11. IMS-China International Conference on Statistics and Probability, Kunming, China, July 2, 2015. Title: On a class of stochastic partial differential equations.

12. Conference on Stochastic Processes and Applied Probability, Jilin University, China, June 5, 2015. Title: Extensions of the I-MMSE relation.

13. 36th Conference on Stochastic Processes and Their Applications, University of Colorado Boulder, July 29, 2013. Title: Exponential asymptotics for time-space Hamiltonians.

14. IMS-SWUFE International Conference on Statistics and Probability, July 2, 2013. Title: The 4/3-variation of the derivative of the self-intersection Brownian local time and related processes.

15. Workshop on Probability & Statistics and Applications, Wuhan Institute of Physics and Mathematics, Chinese Academy of Science, June 19, 2013. Title: Exponential asymptotics for time-space Hamiltonians.

16. Colloquium talk, Lehigh University, November 7, 2012. Title: Asymptotic behavior of the solution of heat equation driven by fractional white noise.