王小捷，中南大學數學與統計學院教授
個人簡歷,在研項目,已完成項目,獲獎情況,國外留學與訪問經歷,International conferences,教育經歷,研究方向,主要論文,
個人簡歷
中南大學數學與統計學院教授，博士生導師。研究方向為隨機偏微分方程、隨機常微分方程數值方法以及計算金融等故慨盼，在隨機常微分方程數值方法與理論、隨機熱傳導方程和隨機波動方程數值方法的構造與分析等方面做出一系列研獄達究成果，論文發表在 “SIAM Journal on Numerical Analysis”、“Mathematics of Computation”、“SIAM Journal on Scientific Computing”、“IMA Journal of Numerical Analysis”、“BIT Numerical Mathematics”、“Journal of Scientific Computing”等享有很高國際學術聲譽的計算數學一流國際刊物。系列研究成果得到來自美國、德國、瑞士、英國、法國、瑞典等眾多歐美已開發國家同行的廣泛關注，並在Memoirs of AMS、Ann Probab、Ann Appl Probab、Transactions of AMS、J. Math. Pures Appl.、Stoch Proc Appl、SIAM J Numer Anal、SIAM Sci Comput、Math Comput、Found Comput Math、IMA J Numer Anal、J Comput Phys等計算數學、機率論、數學綜合國際頂尖期刊在內的眾多刊物上引用。自2015年起受邀擔任《Math Review》評論員，是SIAM Journal on Numerical Analysis、Numerische Mathematik、Mathematics of Computation、IMA Journal of Numerical Analysis、 BIT、 Communications in Mathematical Sciences、Stochastic Partial Differential Equations: Analysis and Computations、Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP)、 Discrete and Continuous Dynamical Systems - Series B、Journal of Mathematical Analysis and Applications、Numerical Algorithms等十餘個國際著名刊物的審稿人。現主持1項國家自然科學基金面上項目和 2015年第二批“中南大學升華育英”人才計畫項目。已主持完成1項國家自然科學基金青年項目、1項蘭祝堡湖南省自然科學基金青年項目、中南大學第五批創新驅動計畫項目、1項中國博士後科學基金特別資助項目和1項中國博士後科學基金面上項目。本人學術交流廣泛，多次應邀訪問瑞士聯邦理工學院(ETH)、中科院數學與系統科學研究院等國內外著名高校或研究府乎承所，多次應邀參加國際學術會議並做大會邀請報告或專題邀請報告。特別地，兩凝仔臘漏次受到世界著名數學研究所——Mittag-Leffler研究所的邀請和資助參加研究所舉辦的隨機偏微分方程數值方法國際研討會並做會議特邀報告。與多名國際著名的隨機微分方程數值分析專家(如Peter Kloeden教授，Stig Larsson教授，Arnulf Jentzen教授，Gabriel Lord教授，David Cohen教授等)有著廣泛而緊密的學術交流和合作。
在研項目
6. 國家自然科學基金面上項目 “兩類隨機發展方程的數疊立拘值分析”，No.11671405, 2017.01-2020.12（主持）
5. 湖南省自然科學基金青年項目 “拋物型隨機微分方程的數值方法研究雄照精危”，No.2016JJ3137, 2016.01-2018.12 (主持)
4. 中南大學第五批創新驅動計畫項目“隨機偏微分方程的高效數值算法研究”，No. 2017CX017, 2017.03-2018.12 (主持)
3. 2015年度第二批“中南大學升華育英”人才計畫項目，2016.05-2021.04 (主持)
2. 國家自然科學基金重大研究計畫集成項目 “隨機哈密爾頓偏微分方程高效數值方法”, No.91630312, 2017.01-2019.12 (參加)
1. 國家自然科學基金面上項目 "隨機微分方程弱逼近理論及套用", No.11571373, 2016.01-2019.12 (參加)
5. 湖南省自然科學基金青年項目 “拋物型隨機微分方程的數值方法研究雄照精危”，No.2016JJ3137, 2016.01-2018.12 (主持)
4. 中南大學第五批創新驅動計畫項目“隨機偏微分方程的高效數值算法研究”，No. 2017CX017, 2017.03-2018.12 (主持)
3. 2015年度第二批“中南大學升華育英”人才計畫項目，2016.05-2021.04 (主持)
2. 國家自然科學基金重大研究計畫集成項目 “隨機哈密爾頓偏微分方程高效數值方法”, No.91630312, 2017.01-2019.12 (參加)
1. 國家自然科學基金面上項目 "隨機微分方程弱逼近理論及套用", No.11571373, 2016.01-2019.12 (參加)
已完成項目
5. 國家自然科學基金青年項目 “非全局Lipschitz條件下的隨機微分方程數值強收斂性研究”，No.11301550, 2014.01-2016.12（主持）
4. 中國博士後科學基金特別資助 “拋物型隨機偏微分方程的數值收斂性研究”，No.2014T70779, 2014.07-2016.03（主持）
3. 中國博士後科學基金面上項目 “半線性拋物型隨機微分方程數值方法的強收斂性研究”，No.2013M531798， 2013.05-2016.03（主持）
2. 國家自然科學基金面上項目“剛性隨機微分方程的數值分析”，No.11171352， 2012.01-2015.12（參加）
1. 國家自然科學基金面上項目“幾類隨機泛函微分方程數值方法的收斂性、穩定性和散逸性”，2009-2011（參加）
4. 中國博士後科學基金特別資助 “拋物型隨機偏微分方程的數值收斂性研究”，No.2014T70779, 2014.07-2016.03（主持）
3. 中國博士後科學基金面上項目 “半線性拋物型隨機微分方程數值方法的強收斂性研究”，No.2013M531798， 2013.05-2016.03（主持）
2. 國家自然科學基金面上項目“剛性隨機微分方程的數值分析”，No.11171352， 2012.01-2015.12（參加）
1. 國家自然科學基金面上項目“幾類隨機泛函微分方程數值方法的收斂性、穩定性和散逸性”，2009-2011（參加）
獲獎情況
2014年湖南省優秀博士學位論文
2016年度中國仿真學會優秀論文獎
2016年度中國仿真學會優秀論文獎
國外留學與訪問經歷
-2017年9月4日－2017年9月11日 受Dr. Janosch Rieger邀請訪問Monash University, Australia
-2015年6月8日－2015年6月15日 受Stig Larsson教授邀請和資助訪問Chalmers University of Technology, Sweden
-2015年5月31日－2015年6月7日 受David Cohen教授邀請和資助訪問Umea University, Sweden
-2013年7月-2013年8月 受Arnulf Jentzen教授邀請和資助訪問瑞士蘇黎世聯邦理工學院(ETH)兩個月
-2010年9月-2011年8月 受國家留學基金委資助在德國法蘭克福大學博士聯合培養一年
-2015年6月8日－2015年6月15日 受Stig Larsson教授邀請和資助訪問Chalmers University of Technology, Sweden
-2015年5月31日－2015年6月7日 受David Cohen教授邀請和資助訪問Umea University, Sweden
-2013年7月-2013年8月 受Arnulf Jentzen教授邀請和資助訪問瑞士蘇黎世聯邦理工學院(ETH)兩個月
-2010年9月-2011年8月 受國家留學基金委資助在德國法蘭克福大學博士聯合培養一年
International conferences
-2019 IMS China, Dalian, July 6-10, 2019 (invited talk in an invited mini-symposium)
-Workshop on Numerical Methods for SPDE: 20 Successful Years and Future Challenges, Institut Mittag-Leffler (IML), Djursholm, Sweden, May 20-24, 2019 (invited speaker)
-The 40th Stochastic Processes and their Applications International Conference, 11–15 June 2018, Gothenburg, Sweden (organizer of a session on numerical SPDEs)
-International Workshop on BSDEs, SPDEs and their Applications, Edinburgh, July 3-7, 2017 ( invited talk in a special session "Numerical approximations and regularity of SPDEs")
-10th International Conference on Computational Physics, 16-20 Jan 2017, Macao (invited talk in a mini-symposium)
-20th IMACS World Congress, 10-14 December 2016, Xiamen (invited talk in a mini-symposium)
-Workshop on Stochastic Numerics, 16-17 April 2016, Huazhong University of Science and Technology (HUST), Wuhan (co-organizer)
-The International Congress on Industrial and Applied Mathematics (ICIAM), Beijing, Aug. 10-14, 2015 (invited talk in a mini-symposium)
-Conference on Advances in Numerical Methods for SPDEs, Djursholm, Sweden, June 16-18, 2015 (invited talk, invited and funded by the Institut Mittag-Leffler)
-International Congress of Mathematicians(ICM), Seoul, Korea, Aug. 13-21, 2014 (20-minute-talk, funded by NIMS of Korea)
-International Conference on Dynamical Systems and Applications (dedicated to Prof. Peter Kloeden on the occasion of his 65th birthday), HUST, Wuhan, China, July 26-30, 2014 (invited talk)
-International Workshop on Numerical Methods of Stochastic Differential Equations, Beijing, Oct.16-19, 2013 (talk)
-3rd International Conference on Numerical Analysis of Differential Equations, Nanjing, Mar.29-31, 2013 (talk)
********** Forthcoming conferences **********
-"Stochastic Computation" workshop at the next Foundations of Computational Mathematics conference (FoCM 2020), Vancouver, Canada, June 15-24, 2020.
-Workshop on Numerical Methods for SPDE: 20 Successful Years and Future Challenges, Institut Mittag-Leffler (IML), Djursholm, Sweden, May 20-24, 2019 (invited speaker)
-The 40th Stochastic Processes and their Applications International Conference, 11–15 June 2018, Gothenburg, Sweden (organizer of a session on numerical SPDEs)
-International Workshop on BSDEs, SPDEs and their Applications, Edinburgh, July 3-7, 2017 ( invited talk in a special session "Numerical approximations and regularity of SPDEs")
-10th International Conference on Computational Physics, 16-20 Jan 2017, Macao (invited talk in a mini-symposium)
-20th IMACS World Congress, 10-14 December 2016, Xiamen (invited talk in a mini-symposium)
-Workshop on Stochastic Numerics, 16-17 April 2016, Huazhong University of Science and Technology (HUST), Wuhan (co-organizer)
-The International Congress on Industrial and Applied Mathematics (ICIAM), Beijing, Aug. 10-14, 2015 (invited talk in a mini-symposium)
-Conference on Advances in Numerical Methods for SPDEs, Djursholm, Sweden, June 16-18, 2015 (invited talk, invited and funded by the Institut Mittag-Leffler)
-International Congress of Mathematicians(ICM), Seoul, Korea, Aug. 13-21, 2014 (20-minute-talk, funded by NIMS of Korea)
-International Conference on Dynamical Systems and Applications (dedicated to Prof. Peter Kloeden on the occasion of his 65th birthday), HUST, Wuhan, China, July 26-30, 2014 (invited talk)
-International Workshop on Numerical Methods of Stochastic Differential Equations, Beijing, Oct.16-19, 2013 (talk)
-3rd International Conference on Numerical Analysis of Differential Equations, Nanjing, Mar.29-31, 2013 (talk)
********** Forthcoming conferences **********
-"Stochastic Computation" workshop at the next Foundations of Computational Mathematics conference (FoCM 2020), Vancouver, Canada, June 15-24, 2020.
教育經歷
[1]2007.9-2012.6
中南大學| 計算數學| 博士學位| 博士研究生畢業
[2]2003.9-2007.7
中南大學| 數學與套用數學| 學士學位| 大學本科畢業
研究方向
- [1] 隨機偏微分方程數值分析
- [2] 隨機常微分方程數值解法
- [3] 計算金融
主要論文
- [1] Ruisheng Qi and Xiaojie Wang. Error estimates of finite element method for semi-linear stochastic strongly damped wave equation [J]. IMA Journal of Numerical Analysis, 2019, 39(3): 1594-1626
- [2] Ruisheng Qi, and Xiaojie Wang. Optimal error estimates of Galerkin finite element methods for stochastic Allen-Cahn equation with additive noise [J]. Journal of Scientific Computing, 2019, 80(2): 1171-1194
- [3] Martin Hutzenthaler, Arnulf Jentzen, and Xiaojie Wang. Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations [J]. Mathematics of Computation, 2018, 87(311): 1353-1413
- [4] Xiaojie Wang, Ruisheng Qi, Fengze Jiang. Sharp mean-square regularity results for SPDEs with fractional noise and optimal convergence rates for the numerical approximations [J]. BIT Numerical Mathematics, 2017, 57(2): 557–585
- [5] Xiaojie Wang. Strong convergence rates of the linear implicit Euler method for the finite element discretization of SPDEs with additive noise [J]. IMA Journal of Numerical Analysis, 2017, 37(2): 965-984
- [6] Rikard Anton, David Cohen, Stig Larsson and Xiaojie Wang. Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise [J]. SIAM Journal on Numerical Analysis, 2016, 54(2): 1093-1119
- [7] Xiaojie Wang. Weak error estimates of the exponential Euler scheme for semi-linear SPDEs without Malliavin calculus [J]. Discrete and Continuous Dynamical Systems-Series A, 2016, 36(1): 481-497
- [8] Xiaojie Wang. An exponential integrator scheme for time discretization of nonlinear stochastic wave equation [J]. Journal of Scientific Computing, 2015, 64(1): 234-263
- [9] Xiaojie Wang, Siqing Gan, and Jingtian Tang.. Higher order strong approximations of semilinear stochastic wave equation with additive space-time white noise [J]. SIAM Journal on Scientific Computing, 2014, 36(6): A2611-A2632
- [10] Xiaojie Wang, Siqing Gan, and Desheng Wang. A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise [J]. BIT Numerical Mathematics, 2012, 52(3): 741-772
在研項目
6. 國家自然科學基金面上項目 “兩類隨機發展方程的數值分析”，No.11671405, 2017.01-2020.12（主持）
5. 湖南省自然科學基金青年項目 “拋物型隨機微分方程的數值方法研究”，No.2016JJ3137, 2016.01-2018.12 (主持)
4. 中南大學第五批創新驅動計畫項目“隨機偏微分方程的高效數值算法研究”，No. 2017CX017, 2017.03-2018.12 (主持)
3. 2015年度第二批“中南大學升華育英”人才計畫項目，2016.05-2021.04 (主持)
2. 國家自然科學基金重大研究計畫集成項目 “隨機哈密爾頓偏微分方程高效數值方法”, No.91630312, 2017.01-2019.12 (參加)
1. 國家自然科學基金面上項目 "隨機微分方程弱逼近理論及套用", No.11571373, 2016.01-2019.12 (參加)
5. 湖南省自然科學基金青年項目 “拋物型隨機微分方程的數值方法研究”，No.2016JJ3137, 2016.01-2018.12 (主持)
4. 中南大學第五批創新驅動計畫項目“隨機偏微分方程的高效數值算法研究”，No. 2017CX017, 2017.03-2018.12 (主持)
3. 2015年度第二批“中南大學升華育英”人才計畫項目，2016.05-2021.04 (主持)
2. 國家自然科學基金重大研究計畫集成項目 “隨機哈密爾頓偏微分方程高效數值方法”, No.91630312, 2017.01-2019.12 (參加)
1. 國家自然科學基金面上項目 "隨機微分方程弱逼近理論及套用", No.11571373, 2016.01-2019.12 (參加)
已完成項目
5. 國家自然科學基金青年項目 “非全局Lipschitz條件下的隨機微分方程數值強收斂性研究”，No.11301550, 2014.01-2016.12（主持）
4. 中國博士後科學基金特別資助 “拋物型隨機偏微分方程的數值收斂性研究”，No.2014T70779, 2014.07-2016.03（主持）
3. 中國博士後科學基金面上項目 “半線性拋物型隨機微分方程數值方法的強收斂性研究”，No.2013M531798， 2013.05-2016.03（主持）
2. 國家自然科學基金面上項目“剛性隨機微分方程的數值分析”，No.11171352， 2012.01-2015.12（參加）
1. 國家自然科學基金面上項目“幾類隨機泛函微分方程數值方法的收斂性、穩定性和散逸性”，2009-2011（參加）
4. 中國博士後科學基金特別資助 “拋物型隨機偏微分方程的數值收斂性研究”，No.2014T70779, 2014.07-2016.03（主持）
3. 中國博士後科學基金面上項目 “半線性拋物型隨機微分方程數值方法的強收斂性研究”，No.2013M531798， 2013.05-2016.03（主持）
2. 國家自然科學基金面上項目“剛性隨機微分方程的數值分析”，No.11171352， 2012.01-2015.12（參加）
1. 國家自然科學基金面上項目“幾類隨機泛函微分方程數值方法的收斂性、穩定性和散逸性”，2009-2011（參加）
獲獎情況
2014年湖南省優秀博士學位論文
2016年度中國仿真學會優秀論文獎
2016年度中國仿真學會優秀論文獎
國外留學與訪問經歷
-2017年9月4日－2017年9月11日 受Dr. Janosch Rieger邀請訪問Monash University, Australia
-2015年6月8日－2015年6月15日 受Stig Larsson教授邀請和資助訪問Chalmers University of Technology, Sweden
-2015年5月31日－2015年6月7日 受David Cohen教授邀請和資助訪問Umea University, Sweden
-2013年7月-2013年8月 受Arnulf Jentzen教授邀請和資助訪問瑞士蘇黎世聯邦理工學院(ETH)兩個月
-2010年9月-2011年8月 受國家留學基金委資助在德國法蘭克福大學博士聯合培養一年
-2015年6月8日－2015年6月15日 受Stig Larsson教授邀請和資助訪問Chalmers University of Technology, Sweden
-2015年5月31日－2015年6月7日 受David Cohen教授邀請和資助訪問Umea University, Sweden
-2013年7月-2013年8月 受Arnulf Jentzen教授邀請和資助訪問瑞士蘇黎世聯邦理工學院(ETH)兩個月
-2010年9月-2011年8月 受國家留學基金委資助在德國法蘭克福大學博士聯合培養一年
International conferences
-2019 IMS China, Dalian, July 6-10, 2019 (invited talk in an invited mini-symposium)
-Workshop on Numerical Methods for SPDE: 20 Successful Years and Future Challenges, Institut Mittag-Leffler (IML), Djursholm, Sweden, May 20-24, 2019 (invited speaker)
-The 40th Stochastic Processes and their Applications International Conference, 11–15 June 2018, Gothenburg, Sweden (organizer of a session on numerical SPDEs)
-International Workshop on BSDEs, SPDEs and their Applications, Edinburgh, July 3-7, 2017 ( invited talk in a special session "Numerical approximations and regularity of SPDEs")
-10th International Conference on Computational Physics, 16-20 Jan 2017, Macao (invited talk in a mini-symposium)
-20th IMACS World Congress, 10-14 December 2016, Xiamen (invited talk in a mini-symposium)
-Workshop on Stochastic Numerics, 16-17 April 2016, Huazhong University of Science and Technology (HUST), Wuhan (co-organizer)
-The International Congress on Industrial and Applied Mathematics (ICIAM), Beijing, Aug. 10-14, 2015 (invited talk in a mini-symposium)
-Conference on Advances in Numerical Methods for SPDEs, Djursholm, Sweden, June 16-18, 2015 (invited talk, invited and funded by the Institut Mittag-Leffler)
-International Congress of Mathematicians(ICM), Seoul, Korea, Aug. 13-21, 2014 (20-minute-talk, funded by NIMS of Korea)
-International Conference on Dynamical Systems and Applications (dedicated to Prof. Peter Kloeden on the occasion of his 65th birthday), HUST, Wuhan, China, July 26-30, 2014 (invited talk)
-International Workshop on Numerical Methods of Stochastic Differential Equations, Beijing, Oct.16-19, 2013 (talk)
-3rd International Conference on Numerical Analysis of Differential Equations, Nanjing, Mar.29-31, 2013 (talk)
********** Forthcoming conferences **********
-"Stochastic Computation" workshop at the next Foundations of Computational Mathematics conference (FoCM 2020), Vancouver, Canada, June 15-24, 2020.
-Workshop on Numerical Methods for SPDE: 20 Successful Years and Future Challenges, Institut Mittag-Leffler (IML), Djursholm, Sweden, May 20-24, 2019 (invited speaker)
-The 40th Stochastic Processes and their Applications International Conference, 11–15 June 2018, Gothenburg, Sweden (organizer of a session on numerical SPDEs)
-International Workshop on BSDEs, SPDEs and their Applications, Edinburgh, July 3-7, 2017 ( invited talk in a special session "Numerical approximations and regularity of SPDEs")
-10th International Conference on Computational Physics, 16-20 Jan 2017, Macao (invited talk in a mini-symposium)
-20th IMACS World Congress, 10-14 December 2016, Xiamen (invited talk in a mini-symposium)
-Workshop on Stochastic Numerics, 16-17 April 2016, Huazhong University of Science and Technology (HUST), Wuhan (co-organizer)
-The International Congress on Industrial and Applied Mathematics (ICIAM), Beijing, Aug. 10-14, 2015 (invited talk in a mini-symposium)
-Conference on Advances in Numerical Methods for SPDEs, Djursholm, Sweden, June 16-18, 2015 (invited talk, invited and funded by the Institut Mittag-Leffler)
-International Congress of Mathematicians(ICM), Seoul, Korea, Aug. 13-21, 2014 (20-minute-talk, funded by NIMS of Korea)
-International Conference on Dynamical Systems and Applications (dedicated to Prof. Peter Kloeden on the occasion of his 65th birthday), HUST, Wuhan, China, July 26-30, 2014 (invited talk)
-International Workshop on Numerical Methods of Stochastic Differential Equations, Beijing, Oct.16-19, 2013 (talk)
-3rd International Conference on Numerical Analysis of Differential Equations, Nanjing, Mar.29-31, 2013 (talk)
********** Forthcoming conferences **********
-"Stochastic Computation" workshop at the next Foundations of Computational Mathematics conference (FoCM 2020), Vancouver, Canada, June 15-24, 2020.
教育經歷
[1]2007.9-2012.6
中南大學| 計算數學| 博士學位| 博士研究生畢業
[2]2003.9-2007.7
中南大學| 數學與套用數學| 學士學位| 大學本科畢業
研究方向
- [1] 隨機偏微分方程數值分析
- [2] 隨機常微分方程數值解法
- [3] 計算金融
主要論文
- [1] Ruisheng Qi and Xiaojie Wang. Error estimates of finite element method for semi-linear stochastic strongly damped wave equation [J]. IMA Journal of Numerical Analysis, 2019, 39(3): 1594-1626
- [2] Ruisheng Qi, and Xiaojie Wang. Optimal error estimates of Galerkin finite element methods for stochastic Allen-Cahn equation with additive noise [J]. Journal of Scientific Computing, 2019, 80(2): 1171-1194
- [3] Martin Hutzenthaler, Arnulf Jentzen, and Xiaojie Wang. Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations [J]. Mathematics of Computation, 2018, 87(311): 1353-1413
- [4] Xiaojie Wang, Ruisheng Qi, Fengze Jiang. Sharp mean-square regularity results for SPDEs with fractional noise and optimal convergence rates for the numerical approximations [J]. BIT Numerical Mathematics, 2017, 57(2): 557–585
- [5] Xiaojie Wang. Strong convergence rates of the linear implicit Euler method for the finite element discretization of SPDEs with additive noise [J]. IMA Journal of Numerical Analysis, 2017, 37(2): 965-984
- [6] Rikard Anton, David Cohen, Stig Larsson and Xiaojie Wang. Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise [J]. SIAM Journal on Numerical Analysis, 2016, 54(2): 1093-1119
- [7] Xiaojie Wang. Weak error estimates of the exponential Euler scheme for semi-linear SPDEs without Malliavin calculus [J]. Discrete and Continuous Dynamical Systems-Series A, 2016, 36(1): 481-497
- [8] Xiaojie Wang. An exponential integrator scheme for time discretization of nonlinear stochastic wave equation [J]. Journal of Scientific Computing, 2015, 64(1): 234-263
- [9] Xiaojie Wang, Siqing Gan, and Jingtian Tang.. Higher order strong approximations of semilinear stochastic wave equation with additive space-time white noise [J]. SIAM Journal on Scientific Computing, 2014, 36(6): A2611-A2632
- [10] Xiaojie Wang, Siqing Gan, and Desheng Wang. A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise [J]. BIT Numerical Mathematics, 2012, 52(3): 741-772
