Convergence of the truncated Euler method for non-autonomous stochastic differential equations with Hölder continuous diffusion coefficients

We studied the convergence of the truncated Euler method for one-dimensional non-autonomous stochastic differential equations with a Hölder continuous diffusion term and obtained its convergence using the Yamada-Watanabe approximation. Compared with earlier work, the main innovation in this paper is to change the type of equation to a non-autonomous stochastic differential equation by introducing a time variable “t”, and make both the diffusion term and drift term Hölder continuous with respect to the time variable “t”. We obtained the convergence rate, and proved that it is dependent on the Hölder order of “t”. Finally, a numerical example is given to illustrate the conclusion.