A partially time-changed Aït-Sahalia model is proposed, where the driving noise is a sub-diffusion process, also known as a time-changed Brownian motion. We prove that the model admits a unique global positive solution and establish positive and negative moment bounds. Finally, a truncated Euler–Maruyama discretization is used to provide numerical illustrations of sample paths and empirical moments.
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Shu et al. (2026) studied this question.
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