Projected Euler method for stochastic delay differential equation under a global monotonicity condition

2018/10/23 by Min Li, Chengming Huang, Li, Min +1
Economics, Econometrics and Finance · Engineering · #Stochastic processes and financial applications #Complex Systems and Time Series Analysis #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1810.09647

Abstract

This paper investigates projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition. This condition admits some equations with highly nonlinear drift and diffusion coefficients. We appropriately generalized the idea of C-stability and B-consistency given by Beyn et al. [J. Sci. Comput. 67 (2016), no. 3, 955-987] to the case with delay. Moreover, the method is proved to be convergent with order (1)/(2) in a succinct way. Finally, some numerical examples are included to illustrate the obtained theoretical results.

Citations

• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Feedback and delays in neurological diseases: A modeling study using dynamical systems

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