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郑伟安，博士，华东师范大学“长江讲座教授”。1980年获华东师范大学数学系概率论与数理统计硕士学位，1981年赴法国斯特拉斯堡大学进修，1984年获法国国家数学科学博士学位。早期工作中的MEYER-ZHENG 弱收敛拓扑以及LYONS-ZHENG 的对称马氏过程分解，都已成为国外出版专著中的经典结果。郑伟安教授长期从事概率论、鞅论、随机微分几何、随机力学、对称马称科夫过程等方面的研究，先后访问了德国比尔费尔德大学、英国爱丁堡大学、法国图卢斯大学、法国巴黎十三大学等，研究成果丰硕。近年来，为了配合华东师大统计系的学科特点，郑伟安教授把研究方向从随机过程的纯理论研究转为过程统计与金融数学，他的研究课题不但有理论价值，应用性也很强。
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1. 随机过程(本科生)
2. 应用随机过程(本科生)
3. 随机分析及其在金融数学中的应用(研究生)
4. 随机微分方程(研究生)
5. 过程统计(研究生)
6. 高等数理统计(研究生)
1. 随机过程
2. 金融数学
3. 过程统计
- 完成项目
近五年在华东师大统计系完成项目:
1. 教育部博士学科点专项科研基金项目《扩散过程的模型选择》, (2003.1--2005.12), 项目批准号: 20020269015
2. 国家自然科学基金项目《马氏过程参数的零界估计及其离散化估计与收敛性》, (2004.1--2006.12), 项目批准号: 10371074,
与上海交通大学联合申请
- 获得奖励
1. 1977年被评为上海市先进科技工作者
2. 1985年获首届许宝禄统计数学奖
3. 1986年获国家自然科学三等奖
4. 1986年获中国青年科技奖
5. 1986年被评为国家级有重大贡献的科技工作者
6. 1987年获霍英东奖
- 期刊杂志(部分代表性论文)
- [1] “Black-Scholes’ Model and Bollinger Bands” (with Wei Liu, Xudong Huang), Pysica A, 2006, 371, 565-571.
[2] Sharp error estimate for maximum likelihood estimator of nonstationary diffusion processes (with Zhiyan Xu),
Acta Math. Sin., 2005, 21, 303-314.
[3] A representation formula for transition probability densities of diffusions and applications (with Zhongmin Qian),
Stochastic Process Appl., 2004, 111(1), 57-76.
[4] Comparison theorem andestimates for transition probability densities of diffusion processes (with Zhongmin Qian,
Francesco Russo), Probability Theory and Related Fields, 2003, 127(3), 388-406.
[5] Rate of convergence in homogenization of parabolic PDEs (with Luis Roman, Xinsheng Zhang),
Math. Phys. Anal. Geom., 2003, 6(2), 113-124.
[6] SPDEs driven by space-time white noise in high dimensions; absolute continuity of the law and convergence
of solutions (with T.S. Zhang), Stochastic and Stochastic Reports, 2003, 75(3), 103-128.
[7] Solution to a class of multidimensional SPDEs (with A.L. Piatnitski, H.Z. Zhao), Int. Math. J., 2003, 3(7), 755-774.
[8] Sharp bounds for transition probability densities of a class of diffusions (with Zhongmin Qian),
C. R. Math. Acad. Sci Paris, 2002, 355(11), 953-957.
[9] Discretizing a backward stochastic differential equation (with Yinnan Zhang), Int. J. Math. Math. Sci.,
2002, 32(2), 103-116.
[10] Brownian time processes: the PDE connection and the half-derivative generator (with Hassan Allouba),
Ann. Prob., 2002, 29(4), 1780-1795.
[11] Stability of time-dependent diffusion semigroups and kernels, Acta. Math. Sin., 1999, 15(4), 575-586 OCT.
[12] Stability and approximations of symmetric diffusion semigroups and Kernels (with Z. Chen, Y. Hu and Z. Qian),
Journal of Functional Analysis, 1998, 152(1), 255-280.
[13] Markov chain approximation to symmetric diffusions (with D. Stroock), Ann. Inst. Henri Poincare,
1997, 33(5), 619-649.
[14] Large deviation results without continuity hypothesis on the diffusion term, Stochastic Analysis and
Applications, World Scientific, 1996, 490-502.
[15] Meyer's topology and Stefan's problem, Seminaire de Probabilite, XXX, LN in Math., 1996, 1626, 108-116.
[16] A phase transition speed estimate in Stefan problem, Proc. Royal Society of Edinburgh, 1996, 126(6), 1341-1347.
[17] Radial part of Brownian-motion on a riemannian manifold (with Liao, M.), Ann. Probab., 1995, 23(1), 173-177 JAN.
[18] Diffusion-processes with nonsmooth diffusion-coefficients and their density-functions (with Lyons, T.J.),
P. Roy. Soc. Edinb. A, 115, 231-242 Part 3-4 1990.
[19] On conditional diffusion-processes (with Lyons, T.J.), P. Roy. Soc. Edinb. A, 115, 243-255 Part 3-4 1990.
[20] On reflecting Brownian-motion -- a weak-convergence approach (with Williams, R.J.), Ann. I. H. Poincare-Pr.,
1990, 26(3), 461-488.
[21] Semimartingale with smooth density -- the problem of nodes, Lect. Notes Math., 1987, 1250, 356-359.
[22] The construction of certain diffusions (with Meyer, P.A.), Lect. Notes Math., 1986, 1204, 334-337.
[23] Tightness results for laws of diffusion-processes application to stochastic mechanics, Ann. I. H. Poincare-Pr.,
1985, 21(2), 103-124.
[24] Non-monotonous stochastic integrals (with Meyer, P.A.), Lect. Notes Math., 1984, 1059, 154-171.
[25] Some results of stochastic mechanics (with Meyer, P.A.), Lect. Notes Math., 1984, 1059, 223-244.
[26] Tightness criteria for laws of semimartingales (with Meyer, P.A.), Ann. I. H. Poincare-Pr., 1984, 20(4), 353-372.
[27] Comments on the convergence of martingales in varieties (with He, S.W.), Lect. Notes Math., 1984, 1059, 174-178.
[28] The martingale convergence theory in riemannian-manifolds (with Darling, R.W., Meyer, P.A.),
Lect. Notes Math., 1983, 986, 187-193.
[29] On the convergence of martingales in a riemannian variety, Z. Wahrscheinlichkeit, 1983, 63(4), 511-515.
[30] On the convergence of continuous semi-martingales in rn and martingales in a manifold (with He, S.W.,
Yan, J.A.), Lect. Notes Math., 1983, 986, 179-184.
[31] The absolute value of a local martingale, Sci. Sin. A -- Math. P. A. T., 1982, 25(6), 561-571.
[32] On local-times of a certain class of semimartingales (with He, S.U.), Chinese Ann. Math. B, 1981, 2(3), 359-364.
- [1] “Black-Scholes’ Model and Bollinger Bands” (with Wei Liu, Xudong Huang), Pysica A, 2006, 371, 565-571.