查看文章

Diffusion models have been thoroughly studied for their use in seeking stochastic differential equation (SDE) solutions and investigating their properties, such as moments and conditional moments, which play significant roles in many real-world applications and are especially beneficial for estimating parameters. In fact, these moments can be directly calculated by applying the transition probability density function (PDF), which is often unknown or unavailable in closed form; the formulas for the conditional moments of the SDE may be unavailable in closed form, as well. In this work, we studied an extended case of Pearson diffusion processes, which are a class of diffusions that have squared diffusion coefficients with time-dependent parameter functions. A complete investigation was carried out for both light- and heavy-tailed Pearson diffusion processes, including Ornstein–Uhlenbeck, Cox–Ingersoll–Ross, Fisher …