The exact discrete model of a system of linear stochastic differential equations driven by fractional noise

2008 ◽  
Vol 29 (6) ◽  
pp. 1019-1031 ◽  
Author(s):  
Theodore Simos
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Model ◽  
Fractional Noise ◽  
Exact Discrete Model

Weak solutions for stochastic differential equations with additive fractional noise

2019 ◽  
Vol 19 (02) ◽  
pp. 1950017
Author(s):  
Zhi Li ◽  
Liping Xu ◽  
Litan Yan
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Weak Solutions ◽  
Linear Growth ◽  
Hurst Parameter ◽  
Pathwise Uniqueness ◽  
Existence Of Weak Solutions ◽  
Fractional Noise ◽  
Linear Growth Condition ◽  
Uniqueness In Law

In this paper, by using a transformation formula for fractional Brownian motion (fBm), we prove the existence of weak solutions to stochastic differential equations driven by an additive fBm with Hurst parameter [Formula: see text] under the linear growth condition. Furthermore, we also consider the uniqueness in law and the pathwise uniqueness of the weak solution.

Gaussian Estimation of a Continuous Time Dynamic Model with Common Stochastic Trends

1996 ◽  
Vol 12 (2) ◽  
pp. 361-373 ◽  
Author(s):  
Theodore Simos
Keyword(s):  
Differential Equations ◽  
Continuous Time ◽  
Discrete Model ◽  
Likelihood Function ◽  
Order System ◽  
Time Dynamic ◽  
First Order ◽  
Stochastic Trends ◽  
Exact Discrete Model ◽  
Gaussian Estimation

We derive the exact discrete model and the Gaussian likelihood function of a first-order system of linear stochastic differential equations driven by an observable vector of stochastic trends and a vector of stationary innovations.

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