Weak solutions for stochastic differential equations with additive fractional noise

2004 ◽  
Vol 70 (4) ◽  
pp. 253-261 ◽  
Author(s):  
Yu. Mishura ◽  
D. Nualart
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Weak Solutions ◽  
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.

scholarly journals On the continuity of weak solutions of backward stochastic differential equations

10.4213/tvp15 ◽  
2007 ◽  
Vol 52 (1) ◽  
pp. 190-199 ◽  
Author(s):  
Rainer Buckdahn ◽  
Rainer Buckdahn ◽  
Ганс-Юрген Энгельберт ◽  
Hans-Jurgen Engelbert
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Weak Solutions ◽  
Backward Stochastic Differential Equations
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