宋健

发布日期: 2024-05-16点击数:

研究领域：Stochastic Partial Differential Equations, Random Matrix Theory, Statisctal Mechanical

Models.

txjsong@hotmail.com

2006.8 -- 2010.5

堪萨斯大学理学博士学位

2018-10--至今数学与交叉科学研究中心

2013.1 -- 2018.8 香港大学

2010.9 -- 2012.12 Rutgers University at New Brunswick

[1] . Hyperbolic Anderson Model 2: Strichartz Estimates and Stratonovich Setting. 2023.

[2] . HITTING PROBABILITIES OF GAUSSIAN RANDOM FIELDS AND COLLISION OF EIGENVALUES OF RANDOM MATRICES. 2023.

[3] . Recent advances on eigenvalues of matrix-valued stochastic processes. Journal of Multivariate Analysis, 188, 2022.

[4] . Skorohod and Stratonovich integrals for controlled processes. 随机过程及其应用, 150, 569-595, 2022.

[5] . ENTROPY FLOW AND DE BRUIJN'S IDENTITY FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRA. PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 35, 369, 2021.

[6] . High-dimensional central limit theorems for a class of particle systems. ELECTRONIC JOURNAL OF PROBABILITY, 26, 2021.

[7] . Fractional stochastic wave equation driven by a Gaussian noise rough in space. BERNOULLI, 26, 2699, 2020.

[8] . HIGH-DIMENSIONAL LIMITS OF EIGENVALUE DISTRIBUTIONS FOR GENERAL WISHART PROCESS. ANNALS OF APPLIED PROBABILITY, 30, 1642, 2020.

[9] . Scaling limit of a directed polymer among a Poisson field of independent walks. Journal of Funtional Analysis, 281, 2021.

[10] . On collision of multiple eigenvalues for matrix-valued Gaussian processes. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Journal, 502, 2021.

[11] . HOLDER CONTINUITY FOR THE PARABOLIC ANDERSON MODEL WITH SPACE-TIME HOMOGENEOUS GAUSSIAN NOISE. Acta Mathematica Scientia, 39, 717, 2019.

[12] . Limit theorems for functionals of two independent Gaussian processes. Stochastic Processes and their Applications, 129, 4791, 2019.

[13] . Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise. ELECTRONIC JOURNAL OF PROBABILITY, 24, 2019.

[14] . Second order Lyapunov exponents for parabolic and hyperbolic Anderson models. BERNOULLI, 25, 3069, 2019.

[15] Ding, Jian. A new correlation inequality for Ising models with external fields. PROBABILITY THEORY AND RELATED FIELDS, 2022.

[16] Choi, Michael C. H.. ENTROPY FLOW AND DE BRUIJN'S IDENTITY FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRA. PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 35, 369, 2021.

[17] Shen, Hao. Scaling limit of a directed polymer among a Poisson field of independent walks. Journal of Funtional Analysis, 281, 2021.

[18] 宋健. High-dimensional central limit theorems for a class of particle systems. ELECTRONIC JOURNAL OF PROBABILITY, 26, 2021.

[19] 宋健. On collision of multiple eigenvalues for matrix-valued Gaussian processes. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Journal, 502, 2021.

[20] 宋健. SPDEs with Colored Gaussian Noise: A Survey. Communications in Mathematics and Statistics, 6, 481, 2018.

[21] 宋健. HIGH-DIMENSIONAL LIMITS OF EIGENVALUE DISTRIBUTIONS FOR GENERAL WISHART PROCESS. ANNALS OF APPLIED PROBABILITY, 30, 1642, 2020.

[22] 宋健. Fractional stochastic wave equation driven by a Gaussian noise rough in space. BERNOULLI, 26, 2699, 2020.

[23] 宋健 and Balan, Raluca M.. HOLDER CONTINUITY FOR THE PARABOLIC ANDERSON MODEL WITH SPACE-TIME HOMOGENEOUS GAUSSIAN NOISE. Acta Mathematica Scientia, 39, 717, 2019.

[24] 宋健 and Balan, Raluca M.. Second order Lyapunov exponents for parabolic and hyperbolic Anderson models. BERNOULLI, 25, 3069, 2019.

[25] 宋健. Limit theorems for functionals of two independent Gaussian processes. Stochastic Processes and their Applications, 129, 4791, 2019.

[26] 宋健 and Balan, Raluca M.. Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise. ELECTRONIC JOURNAL OF PROBABILITY, 24, 2019.

[27] 宋健. NONLINEAR FEYNMAN-KAC FORMULAS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH SPACE-TIME NOISE. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 51, 955, 2019.

[28] 宋健. SPDEs with Colored Gaussian Noise: A Survey. Communications in Mathematics and Statistics, 2018.

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

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

[31] On a class of stochastic partial differential equations. Stochastic Processes and Their Applications, 127 (2017), no. 1, 37-79.,

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

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

[34] X. Chen , Y. Hu , J. Song and F. Xing. Exponential asymptotics for time-space Hamiltonians.. Ann. Inst. Henri Poincar Probab. Stat. 51 (2015), no. 4, 1529-1561.,

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

[36] 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.,

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

[38] Y. Hu , D. Nualart and J. Song. A nonlinear stochastic heat equation: H ̈older continuity and smoothness of the density of the solu. Stochastic Processes and their Applications, Vol 123, Issue 3, March 2013, Pages 1083-1103.,

[39] 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,

[40] Asymptotic behavior of the solution of heat equation driven by fractional white noise.. Statistics and Probability Letters 2012. 82 no. 3, 614-620.,

[41] 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,

[42] Y. Hu , D. Ocone and J. Song. Some results on backward stochastic differential equations driven by fractional Brownian motions. Stochastic analysis and applications to fi- nance, 225-242,

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

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

[1]复杂随机系统控制相关问题研究,2023/12/01,2028/11/30,

[2]伊辛模型的数学理论,2023/01/01,2024/12/31,

[3]（包干项目）拟独立序列的极限定理及其在金融中的应用,2021/12/23,2024/12/31,

[4]部分可观测平均场正倒向随机系统的控制与博弈,2020/12/16,2023/12/31,

[5]关于矩阵值随机过程特征值的若干研究,2020/09/18,2024/12/31,

[6]非线性随机系统的控制与对策,2019/11/18,2024/12/31,