Strong convergence of split-step backward Euler method for stochastic age-dependent capital system with Markovian switching

In this paper, we present and analyze the split-step backward Euler method for the stochastic capital system with Markovian switching. Under the one-sided local Lipschitz condition on the drift and local Lipschitz condition on the diffusion, we prove the split-step backward Euler method converges with strong order of one half to the true solution. A numerical example is provided to illustrate the theoretical results.