When randomising the timestep sizes in Euler‘s method, we need to linearly interpolate between subsequent timepoints to approximate the ODE solution at times of interest. The resulting piecewise linear path can sometimes be written as a Markov process.
I have analysed this Markov process:
academic.oup.com
The random timestep Euler method and its continuous dynamics
Abstract. Ordinary differential equation (ODE) solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differentia
