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

Key Points

• The research aims to analyze the convergence behavior of jump-diffusion processes influenced by Markovian switching.
• Investigation of jump-diffusion processes using the truncated Euler–Maruyama method.
• Assumed drift and diffusion coefficients follow a Khasminskii-type condition.
• Analyzed the performance of the TEM method concerning mean square stability and boundedness.
• Derived the convergence rate for the TEM method.
• Demonstrated that the TEM method maintains mean square stability of the jump-diffusion process.
• Shown that the process remains asymptotically bounded under the specified conditions.

Abstract