Density Estimates for Solutions of Stochastic Functional Differential Equations

2019 ◽  
Vol 39 (4) ◽  
pp. 955-970
Author(s):  
Nguyen Tien Dung ◽  
Ta Cong Son ◽  
Tran Manh Cuong ◽  
Nguyen Van Tan ◽  
Trinh Nhu Quynh
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Density Estimates ◽  
Functional Differential ◽  
Stochastic Functional

scholarly journals Smoothness and Gaussian Density Estimates for Stochastic Functional Differential Equations with Fractional Noise

2020 ◽  
Vol 8 (4) ◽  
pp. 822-833
Author(s):  
Nguyen Van Tan
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Malliavin Calculus ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Density Estimates ◽  
Fractional Noise ◽  
Gaussian Density ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we study the density of the solution to a class of stochastic functional differential equations driven by fractional Brownian motion. Based on the techniques of Malliavin calculus, we prove the smoothness and establish upper and lower Gaussian estimates for the density.

Harnack inequalities and applications for functional SDEs driven by fractional Brownian motion

2014 ◽  
Vol 22 (4) ◽  
Author(s):  
Zhi Li ◽  
Jiaowan Luo
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Functional Differential Equations ◽  
Hurst Parameter ◽  
Stochastic Functional Differential Equations ◽  
Harnack Inequalities ◽  
Functional Differential ◽  
Stochastic Functional

AbstractIn this paper, Harnack inequalities are established for stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter

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