scholarly journals Moment boundedness of linear stochastic delay differential equations with distributed delay

2014 ◽  
Vol 124 (1) ◽  
pp. 586-612 ◽  
Author(s):  
Zhen Wang ◽  
Xiong Li ◽  
Jinzhi Lei
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Distributed Delay ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Moment Boundedness ◽  
Delay Differential

scholarly journals A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yanli Zhou ◽  
Yonghong Wu ◽  
Xiangyu Ge ◽  
B. Wiwatanapataphee
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Approximation Scheme ◽  
Jump Diffusion ◽  
Mathematical Finance ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Taylor Approximation ◽  
Wide Range ◽  
Delay Differential

Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. Solution of the underlying initial value problems is important for the understanding and control of many phenomena and systems in the real world. In this paper, we construct a robust Taylor approximation scheme and then examine the convergence of the method in a weak sense. A convergence theorem for the scheme is established and proved. Our analysis and numerical examples show that the proposed scheme of high order is effective and efficient for Monte Carlo simulations for jump-diffusion stochastic delay differential equations.

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