Stability of the Stochastic θ-Method for Super-Linear Stochastic Differential Equations with Unbounded Delay (Journal of Computational Mathematics, 2019)
This paper deals with numerical stability properties of super-linear stochastic differential equations with unbounded delay. Sufficient conditions for mean square and almost suredecay stability of the above system and its stochastic θ-method approximation are investigated in this paper. The author establishes numerical stability under a monotone-typecondition in unbounded delay setting. An example is presented to illustrate the result.
Keywords: Unbounded delay; Monotone condition; Polynomial condition; Stochastic θ-method; Decay stability.