Weak convergence of functional stochastic differential equations with variable delays

2013 ◽  
Vol 83 (11) ◽  
pp. 2592-2599 ◽  
Author(s):  
Li Tan ◽  
Wei Jin ◽  
Zhenting Hou
Keyword(s):  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Variable Delays

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 A Compensated Numerical Method for Solving Stochastic Differential Equations with Variable Delays and Random Jump Magnitudes

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Ying Du ◽  
Changlin Mei
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Mean Square ◽  
Variable Delays ◽  
Mean Square Stability ◽  
The Mean ◽  
Random Jump

Stochastic differential equations with jumps are of a wide application area especially in mathematical finance. In general, it is hard to obtain their analytical solutions and the construction of some numerical solutions with good performance is therefore an important task in practice. In this study, a compensated split-stepθmethod is proposed to numerically solve the stochastic differential equations with variable delays and random jump magnitudes. It is proved that the numerical solutions converge to the analytical solutions in mean-square with the approximate rate of 1/2. Furthermore, the mean-square stability of the exact solutions and the numerical solutions are investigated via a linear test equation and the results show that the proposed numerical method shares both the mean-square stability and the so-called A-stability.

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>

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