Backward uniqueness of 3D MHD‐ α model driven by linear multiplicative Gaussian noise

2019 ◽  
Vol 42 (18) ◽  
pp. 6522-6536 ◽  
Author(s):  
Rangrang Zhang
Keyword(s):  
Gaussian Noise ◽  
Model Driven ◽  
Backward Uniqueness

The mean first-passage time in simplified FitzHugh–Nagumo neural model driven by correlated non-Gaussian noise and Gaussian noise

2018 ◽  
Vol 32 (28) ◽  
pp. 1850339 ◽  
Author(s):  
Yong-Feng Guo ◽  
Bei Xi ◽  
Fang Wei ◽  
Jian-Guo Tan
Keyword(s):  
Gaussian Noise ◽  
Noise Intensity ◽  
First Passage Time ◽  
Neural Model ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Model Driven ◽  
The Mean ◽  
Non Gaussian

In this paper, the mean first-passage time (MFPT) in simplified FitzHugh–Nagumo (FHN) neural model driven by correlated multiplicative non-Gaussian noise and additive Gaussian white noise is studied. Firstly, using the path integral approach and the unified colored-noise approximation (UCNA), the analytical expression of the stationary probability distribution (SPD) is derived, and the validity of the approximation method employed in the derivation is checked by performing numerical simulation. Secondly, the expression of the MFPT of the system is obtained by applying the definition and the steepest-descent method. Finally, the effects of the multiplicative noise intensity D, the additive noise intensity Q, the noise correlation time [Formula: see text], the cross-correlation strength [Formula: see text] and the non-Gaussian noise deviation parameter q on the MFPT are discussed.

High order Anderson parabolic model driven by rough noise in space

2021 ◽  
pp. 2150052
Author(s):  
Qiyong Cao ◽  
Hongjun Gao
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Gaussian Noise ◽  
Existence And Uniqueness ◽  
Space Variable ◽  
Index Formula ◽  
Hurst Index ◽  
Parabolic Model ◽  
Time And Space ◽  
Model Driven

In this paper, we concern the fourth parabolic model on [Formula: see text] driven by a multiplicative Gaussian noise which behaves like fractional Brownian motion in time and space with Hurst index [Formula: see text] and [Formula: see text], respectively. The existence and uniqueness of mild solution in Skorohod sense are proved, and the weak intermittency is obtained by estimating [Formula: see text]th ([Formula: see text]) moment of the solution. Moreover, the Hölder continuity can be obtained for the time and space variable.

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