DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

doi:10.1007/s10473-019-0404-2

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

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. 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. 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/Abstract

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

中图分类号:

34K50

Nguyen Tien DUNG, Ta Cong SON, Tran Manh CUONG, Nguyen Van TAN, Trinh Nhu QUYNH. DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2019, 39(4): 955-970.

Nguyen Tien DUNG, Ta Cong SON, Tran Manh CUONG, Nguyen Van TAN, Trinh Nhu QUYNH. DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia,Series B, 2019, 39(4): 955-970.

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DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

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