Abstract
In this paper, we establish a partially truncated Euler–Maruyama scheme for highly nonlinear and nonautonomous neutral stochastic differential delay equations with Markovian switching. We investigate the strong convergence rate and almost sure exponential stability of the numerical solutions under the generalized Khasminskii-type condition.
Highlights
Stochastic differential equations play an important role in various fields, such as biology, chemistry, and finance [3, 20, 27]
Many stochastic systems depend on the present and past states, and contain derivatives with delays and the function itself, which can be described by neutral stochastic differential delay equations (NSDDEs) [20]
Kolmanovskii et al [12] established a fundamental theory for neutral stochastic differential delay equations with Markovian switching (NSDDEwMSs) and discussed some important properties of the solutions
Summary
Stochastic differential equations play an important role in various fields, such as biology, chemistry, and finance [3, 20, 27]. Wu and Mao [34] showed the convergence of EM method for neutral stochastic functional differential equations. Guo et al [7] discussed the convergence rate of the truncated EM method for stochastic differential delay equations. In [38], the partially truncated EM method for stochastic differential delay equations was proposed. Cong et al [5] used the partially truncated EM method to get the convergence rate and almost sure exponential stability of highly nonlinear SDDEwMSs. Tan and Yuan in [33] showed the convergence rates of the theta-method for nonlinear neutral stochastic differential delay equations driven by Brownian motion and Poisson jumps, but the stability was not analyzed as time goes to infinity.
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