Tamed-Euler method for nonlinear switching diffusion systems with locally Hölder diffusion coefficients

It is widely known that stochastic differential equations with Markovian switching, involving terms without Lipschitz continuity like $|u{|}^{1/2+\alpha }$ for $\alpha \in [0,1/2)$, are of great practical value in many fields such as finance and biology. In this paper, we develop the tamed Euler-Maruyama schemes for switching diffusion systems modulated by a Markov chain, under the circumstances that drift coefficient satisfies the locally Lipschitz condition and diffusion coefficient satisfies the locally Hölder continuous condition. Moreover, we obtain the rate of convergence of the numerical algorithm not only at time $T$ but also over the time interval $[0,T]$. Finally we give the numerical experiments to illustrate the theoretical results.