数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (4): 955-970.doi: 10.1007/s10473-019-0404-2

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DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

Nguyen Tien DUNG1, Ta Cong SON2, Tran Manh CUONG2, Nguyen Van TAN3, Trinh Nhu QUYNH4   

  1. 1. Department of Mathematics, FPT University, Hoa Lac High Tech Park, Hanoi, Vietnam;
    2. Department of Mathematics, VNU Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam;
    3. Department of Foundation, Academy of Cryptography Techniques, 141 Chien Thang, Thanh Tri, Hanoi, Vietnam;
    4. Military Information Technology Institute, 17 Hoang Sam, Cau Giay, Hanoi, Vietnam
  • 收稿日期:2017-12-23 修回日期:2018-04-19 出版日期:2019-08-25 发布日期:2019-09-12
  • 通讯作者: Nguyen Tien DUNG E-mail:dungnt@fpt.edu.vn
  • 基金资助:
    The first author is supported by Viet Nam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2015.15. The third and second authors are supported by the Vietnam National University, Hanoi (QG.16.09).

DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

Nguyen Tien DUNG1, Ta Cong SON2, Tran Manh CUONG2, Nguyen Van TAN3, Trinh Nhu QUYNH4   

  1. 1. Department of Mathematics, FPT University, Hoa Lac High Tech Park, Hanoi, Vietnam;
    2. Department of Mathematics, VNU Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam;
    3. Department of Foundation, Academy of Cryptography Techniques, 141 Chien Thang, Thanh Tri, Hanoi, Vietnam;
    4. Military Information Technology Institute, 17 Hoang Sam, Cau Giay, Hanoi, Vietnam
  • Received:2017-12-23 Revised:2018-04-19 Online:2019-08-25 Published:2019-09-12
  • Supported by:
    The first author is supported by Viet Nam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2015.15. The third and second authors are supported by the Vietnam National University, Hanoi (QG.16.09).

摘要: In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the density.

关键词: Stochastic functional differential equations, density estimates, Malliavin calculus

Abstract: In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the density.

Key words: Stochastic functional differential equations, density estimates, Malliavin calculus

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