Summary: We discuss the Malliavin differentiability of a particular class of Feller diffusions, which we call \(\delta\)-diffusions. This class is given by \[ d\nu_t=\kappa(\theta-\nu_t))dt \eta \nu_t^{\delta}d\mathbb W_t^2,\;\;\delta\in[1/2,1] \] and appears to be of relevance in finance, in particular in interest and foreign-exchange models, as well as in the context of stochastic volatility models. We extend the result obtained in [E. Alòs and the first author, Adv. Appl. Probab. 40, No. 1, 144–162 (2008; Zbl 1137.91422)] for \(\delta=\frac{1}{2}\) and proof Malliavin differentiability for all \(\delta \in [\frac{1}{2},1]\).
For the entire collection see [Zbl 1253.00011].