An efficient approximation scheme for a class of stochastic differential equations

2005 ◽  
pp. 69-78 ◽  
Author(s):  
J. M. C. Clark
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Approximation Scheme ◽  
Efficient Approximation

A Note on the Carathéodory Approximation Scheme for Stochastic Differential Equations under G-Brownian Motion

2012 ◽  
Vol 67 (12) ◽  
pp. 699-704 ◽  
Author(s):  
Faiz Faizullah
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Approximation Scheme ◽  
Approximate Solutions ◽  
Existence And Uniqueness Theorem ◽  
Vector Valued

In this note, the Carathéodory approximation scheme for vector valued stochastic differential equations under G-Brownian motion (G-SDEs) is introduced. It is shown that the Carathéodory approximate solutions converge to the unique solution of the G-SDEs. The existence and uniqueness theorem for G-SDEs is established by using the stated method.

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>

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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