Mean-square dissipativity of several numerical methods for stochastic differential equations with jumps

作者：Ma, Qiang; Ding, Deqiong; Ding, Xiaohua^*

来源：Applied Numerical Mathematics, 2014, 82: 44-50.

DOI：10.1016/j.apnum.2013.10.010

• Mean-square dissipativity
• Stochastic differential equations with jumps
• Compensated numerical methods
• Non-compensated numerical methods

This paper focuses on mean-square dissipativity of several numerical methods applied to a class of stochastic differential equations with jumps. The conditions under which the underlying systems are mean-square dissipative are given. It is shown that the mean-square dissipativity is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce mean-square dissipativity under a stepsize constraint. Those results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of mean-square dissipativity.

• 出版日期2014-8
• 单位哈尔滨工业大学