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

Strong rate of convergence for the Euler–Maruyama approximation of one-dimensional stochastic differential equations involving the local time at point zero

2018 ◽  
Vol 24 (4) ◽  
pp. 249-262
Author(s):  
Mohsine Benabdallah ◽  
Kamal Hiderah
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Local Time ◽  
Diffusion Coefficients ◽  
One Dimensional ◽  
And Diffusion

Abstract We present the Euler–Maruyama approximation for one-dimensional stochastic differential equations involving the local time at point zero. Also, we prove the strong convergence of the Euler–Maruyama approximation whose both drift and diffusion coefficients are Lipschitz. After that, we generalize to the non-Lipschitz case.

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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