Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps. (23rd July 2014)

• Record Type: Journal Article
• Authors: Du, Ying; Mei, Changlin
• Other Names: Han Maoan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-07-23
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/159107
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : To realize the applications of stochastic differential equations with jumps, much attention has recently been paid to the construction of efficient numerical solutions of the equations. Considering the fact that the use of the explicit methods often results in instability and inaccurate approximations in solving stochastic differential equations, we propose two implicit methods, the θ -Taylor method and the balanced θ -Taylor method, for numerically solving the stochastic differential equation with jumps and prove that the numerical solutions are convergent with strong order 1.0. For a linear scalar test equation, the mean-square stability regions of the methods are derived. Finally, numerical examples are given to evaluate the performance of the methods.