Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process

Bernoulli ◽  
2022 ◽  
Vol 28 (1) ◽  
Author(s):  
Xiaobin Sun ◽  
Longjie Xie ◽  
Yingchao Xie
Keyword(s):  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Convergence Rates ◽  
Stable Process ◽  
Strong And Weak Convergence

Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the local times of the unknown process

2016 ◽  
Vol 22 (4) ◽  
Author(s):  
Mohsine Benabdallah ◽  
Youssfi Elkettani ◽  
Kamal Hiderah
Keyword(s):  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Local Time ◽  
Local Times ◽  
One Dimensional ◽  
Strong And Weak Convergence

AbstractIn this paper, we consider both, the strong and weak convergence of the Euler–Maruyama approximation for one-dimensional stochastic differential equations involving the local times of the unknown process. We use a transformation in order to remove the local timeHere

Moderate deviation principle for multivalued stochastic differential equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
Author(s):  
Hua Zhang
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Moderate Deviation ◽  
Reflected Brownian Motion ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

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