Our effort is to develop a criterion on almost surely exponential stability of numerical solution to stochastic pantograph differential equations, with the help of the discrete semimartingale convergence theorem and the technique used in stable analysis of the exact solution. We will prove that the Euler-Maruyama (EM) method can preserve almost surely exponential stability of stochastic pantograph differential equations under the linear growth conditions. And the backward EM method can reproduce almost surely exponential stability for highly nonlinear stochastic pantograph differential equations. A highly nonlinear example is provided to illustrate the main theory.
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R ChinaHarbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Fan, Zhencheng
Song, Minghui
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Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R ChinaHarbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Song, Minghui
Liu, Mingzhu
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机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R ChinaHarbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R ChinaHarbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Fan, Zhencheng
Song, Minghui
论文数: 0引用数: 0
h-index: 0
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R ChinaHarbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Song, Minghui
Liu, Mingzhu
论文数: 0引用数: 0
h-index: 0
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R ChinaHarbin Inst Technol, Dept Math, Harbin 150001, Peoples R China