Articles

DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Nguyen Tien DUNG ,
  • Ta Cong SON ,
  • Tran Manh CUONG ,
  • Nguyen Van TAN ,
  • Trinh Nhu QUYNH
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  • 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 date: 2017-12-23

  Revised date: 2018-04-19

  Online 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).

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.

Cite this article

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 . DOI: 10.1007/s10473-019-0404-2

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