Stochastic Differential Equations with Additive Fractional Noise and Locally Unbounded Drift

2003 ◽  
pp. 353-365 ◽  
Author(s):  
David Nualart ◽  
Youssef Ouknine
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Noise

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.

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law
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