• Corpus ID: 119331212

Multilinear processes in Banach space

@inproceedings{Benth2018MultilinearPI,
  title={Multilinear processes in Banach space},
  author={Fred Espen Benth and Nils Detering and Paul Kruhner},
  year={2018}
}
A process (X(t))t≥0 taking values in R d is called a polynomial process if for every polynomial p of degree n on R, there exists another polynomial q of degree at most n such that E[p(X(t)) |Fs] = q(X(s)) for any t ≥ s ≥ 0. Based on multilinear maps we extend the notion of polynomial processes to a general Banach space B, to form a class of multilinear processes. If B is a Banach algebra and one restricts to multilinear maps being products, our notion of a multilinear process coincides with a… 
Infinite-dimensional polynomial processes
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
Abstract polynomial processes.
We suggest a novel approach to polynomial processes solely based on a polynomial action operator. With this approach, we can analyse such processes on general state spaces, going far beyond Banach
Infinite dimensional affine processes
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.

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