The Truncated EM Method of Jump Diffusions with Markovian Switching: A Case Study of Music Signals

This paper investigates the strong convergence of jump-diffusion processes with Markovian switching using the truncated Euler–Maruyama (TEM) method. Under the assumption that the drift and diffusion coefficients satisfy a Khasminskii-type condition and the jump coefficient meets a linear growth condition, we derive the convergence rate. Furthermore, we demonstrate that the TEM method effectively preserves both the mean square stability and the asymptotic boundedness of the underlying jump-diffusion process. A case study involving music signals is provided to illustrate the theoretical findings.