scholarly journals A general drift estimation procedure for stochastic differential equations with additive fractional noise

2020 ◽  
Vol 14 (1) ◽  
pp. 1075-1136 ◽  
Author(s):  
Fabien Panloup ◽  
Samy Tindel ◽  
Maylis Varvenne
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Estimation Procedure ◽  
Fractional Noise ◽  
Drift Estimation

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.

THE EXACT DISCRETE MODEL OF A THIRD-ORDER SYSTEM OF LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH OBSERVABLE STOCHASTIC TRENDS

2009 ◽  
Vol 13 (5) ◽  
pp. 656-672 ◽  
Author(s):  
Theodore Simos
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Initial Conditions ◽  
Time Lag ◽  
Estimation Procedure ◽  
Discrete Models ◽  
Order System ◽  
Third Order ◽  
Time Model ◽  
Stochastic Trends

The objective of this paper is to develop closed-form formulae for the exact discretization of a third-order system of stochastic differential equations, with fixed initial conditions, driven by observable stochastic trends and white noise innovations. The model provides a realistic alternative to first- and second-order differential equation specifications of the time lag distribution, forming the basis of a testing and estimation procedure. The exact discrete models, derived under two sampling schemes with either stock or flow variables, are put into a system error correction form that preserves the information of the underlying continuous time model regarding the order of integration and the dimension of cointegration space.

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