Affine pure-jump processes on positive Hilbert–Schmidt operators

We show the existence of a broad class affine Markov processes on cone positive self-adjoint Hilbert–Schmidt operators. Such are well-suited as infinite-dimensional stochastic covariance models. The we consider is an analogue semi-definite and symmetric matrices studied in Cuchiero et al. (2011). As finite-dimensional case, construct allow for drift depending linearly state, well jumps governed by jump measure that depends state. fact operators has empty interior calls new approach to proving existence: instead using standard localization techniques, employ theory generalized Feller semigroups introduced Dörsek Teichmann (2010) further developed (2020). Our requires second moment condition measures involved, consequently, obtain explicit formulas first moments process.