Existence of weak solutions for stochastic differential equations and martingale solutions for stochastic semilinear equations

1999 ◽  
Vol 7 (3) ◽  
Author(s):  
L. GAWARECKI ◽  
V. MANDREKAR ◽  
P. RICHARD
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Weak Solutions ◽  
Existence Of Weak Solutions ◽  
Semilinear Equations ◽  
Martingale Solutions

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.

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