Infinite-dimensional polynomial processes

@article{Cuchiero2019InfinitedimensionalPP,
  title={Infinite-dimensional polynomial processes},
  author={Christa Cuchiero and Sara Svaluto-Ferro},
  journal={Finance and Stochastics},
  year={2019},
  volume={25},
  pages={383-426}
}
We introduce polynomial processes taking values in an arbitrary Banach space B ${B}$ via their infinitesimal generator L $L$ and the associated martingale problem. We obtain two representations of the (conditional) moments in terms of solutions of a system of ODEs on the truncated tensor algebra of dual respectively bidual spaces. We illustrate how the well-known moment formulas for finite-dimensional or probability-measure-valued polynomial processes can be deduced in this general framework… 
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Measure-valued affine and polynomial diffusions
TLDR
It is shown the so-called moment formula, i.e. a representation of the conditional marginal moments via a system of finite dimensional linear PDEs, and characterize the corresponding infinitesimal generators and obtain a representation analogous to polynomial diffusions on R+, in cases where their domain is large enough.
Abstract polynomial processes.
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