scholarly journals Weak convergence in the Prokhorov metric of methods for stochastic differential equations

2009 ◽  
Vol 30 (2) ◽  
pp. 579-594 ◽  
Author(s):  
B. Charbonneau ◽  
Y. Svyrydov ◽  
P. F. Tupper
Keyword(s):  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Prokhorov Metric

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.

scholarly journals Weak Convergence Analysis and Improved Error Estimates for Decoupled Forward-Backward Stochastic Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 848
Author(s):  
Wei Zhang ◽  
Hui Min
Keyword(s):  
Differential Equation ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Convergence Analysis ◽  
Error Estimates ◽  
Taylor Expansion ◽  
Backward Stochastic Differential Equations ◽  
Error Terms

In this paper, we mainly investigate the weak convergence analysis about the error terms which are determined by the discretization for solving the stochastic differential equation (SDE, for short) in forward-backward stochastic differential equations (FBSDEs, for short), which is on the basis of Itô Taylor expansion, the numerical SDE theory, and numerical FBSDEs theory. Under the weak convergence analysis of FBSDEs, we further establish better error estimates of recent numerical schemes for solving FBSDEs.

scholarly journals Weak convergence of delay SDEs with applications to Carathéodory approximation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ta Cong Son ◽  
Nguyen Tien Dung ◽  
Nguyen Van Tan ◽  
Tran Manh Cuong ◽  
Hoang Thi Phuong Thao ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Malliavin Calculus ◽  
Time Delays ◽  
Approximation Scheme ◽  
Explicit Estimate ◽  
Fundamental Class

<p style='text-indent:20px;'>In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin calculus, we obtain an explicit estimate for the rate of convergence. An application to the Carathéodory approximation scheme of stochastic differential equations is provided as well.</p>

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

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law
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