The role of slow manifolds in parameter estimation for a multiscale stochastic system with α-stable Lévy noise

2020 ◽  
Vol 61 (7) ◽  
pp. 072701
Author(s):  
Ying Chao ◽  
Pingyuan Wei ◽  
Jinqiao Duan
Keyword(s):  
Parameter Estimation ◽  
Stochastic System ◽  
Lévy Noise ◽  
Slow Manifolds ◽  
Levy Noise

scholarly journals Slow manifolds for a nonlocal fast-slow stochastic system with stable Lévy noise

2019 ◽  
Vol 60 (9) ◽  
pp. 091501
Author(s):  
Hina Zulfiqar ◽  
Shenglan Yuan ◽  
Ziying He ◽  
Jinqiao Duan
Keyword(s):  
Stochastic System ◽  
Lévy Noise ◽  
Slow Manifolds ◽  
Levy Noise

Data assimilation and parameter estimation for a multiscale stochastic system withα-stable Lévy noise

2017 ◽  
Vol 2017 (11) ◽  
pp. 113401 ◽  
Author(s):  
Yanjie Zhang ◽  
Zhuan Cheng ◽  
Xinyong Zhang ◽  
Xiaoli Chen ◽  
Jinqiao Duan ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Stochastic System ◽  
Lévy Noise ◽  
Levy Noise

Mean-square stability of stochastic system with Markov jump and Lévy noise via adaptive control

2020 ◽  
Author(s):  
Mengling Li ◽  
Feiqi Deng ◽  
Xiaofeng Zheng ◽  
Jinnan Luo
Keyword(s):  
Adaptive Control ◽  
Stochastic System ◽  
Lévy Noise ◽  
Mean Square ◽  
Markov Jump ◽  
Mean Square Stability ◽  
Levy Noise

scholarly journals Barrier crossing driven by Lévy noise: Universality and the role of noise intensity

2007 ◽  
Vol 75 (4) ◽  
Author(s):  
Aleksei V. Chechkin ◽  
Oleksii Yu. Sliusarenko ◽  
Ralf Metzler ◽  
Joseph Klafter
Keyword(s):  
Noise Intensity ◽  
Lévy Noise ◽  
Barrier Crossing ◽  
Levy Noise

Slow manifolds for dynamical systems with non-Gaussian stable Lévy noise

2019 ◽  
Vol 17 (03) ◽  
pp. 477-511 ◽  
Author(s):  
Shenglan Yuan ◽  
Jianyu Hu ◽  
Xianming Liu ◽  
Jinqiao Duan
Keyword(s):  
Biological Sciences ◽  
Dynamical Systems ◽  
Scale Parameter ◽  
Lévy Noise ◽  
Stochastic Dynamical Systems ◽  
Time Dynamics ◽  
Slow Manifolds ◽  
Long Time ◽  
Non Gaussian ◽  
Levy Noise

This work is concerned with the dynamics of a class of slow–fast stochastic dynamical systems driven by non-Gaussian stable Lévy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, and then we eliminate the fast variables to reduce the dimensions of these stochastic dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps to investigate long time dynamics. The approximations of slow manifolds with error estimate in distribution are also established. Furthermore, we corroborate these results by three examples from biological sciences.

Parameter Estimation for the Discretely Observed Vasicek Model with Small Fractional Lévy Noise

2020 ◽  
Vol 36 (4) ◽  
pp. 443-461
Author(s):  
Guang Jun Shen ◽  
Qing Bo Wang ◽  
Xiu Wei Yin
Keyword(s):  
Parameter Estimation ◽  
Lévy Noise ◽  
Vasicek Model ◽  
Levy Noise
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