scholarly journals Successive Approximation of SFDEs with Finite Delay Driven byG-Brownian Motion

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Litan Yan ◽  
Qinghua Zhang
Keyword(s):  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Call Option ◽  
Stochastic Functional Differential Equations ◽  
European Call Option ◽  
Finite Delay ◽  
Carathéodory Conditions ◽  
Functional Differential ◽  
Stochastic Functional

We consider the stochastic functional differential equations with finite delay driven byG-Brownian motion. Under the global Carathéodory conditions we prove the existence and uniqueness, and as an application, we price the European call option when the underlying asset's price follows such an equation.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN Lp(Ω, Ch)

2009 ◽  
Vol 09 (04) ◽  
pp. 597-612
Author(s):  
HAIBO BAO ◽  
DAQING JIANG
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Uniqueness Of Solutions ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we shall consider the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay in Lp(Ω, Ch) space: [Formula: see text] where we assume f : R+ × Lp(Ω, Ch) → Lp(Ω, Rn), g : R+ × Lp(Ω, Ch) → Lp(Ω, L(Rm, Rn)), p > 2, and B(t) is a given m-dimensional Brownian motion.

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

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.

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