• Corpus ID: 119331212

Multilinear processes in Banach space

  title={Multilinear processes in Banach space},
  author={Fred Espen Benth and Nils Detering and Paul Kruhner},
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
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.


Vector Integration and Stochastic Integration in Banach Spaces
This article deals with vector integration and stochastic integration in Banach spaces. In particular, it considers the theory of integration with respect to vector measures with finite semivariation
Representation of Infinite-Dimensional Forward Price Models in Commodity Markets
We study the forward price dynamics in commodity markets realised as a process with values in a Hilbert space of absolutely continuous functions defined by Filipović (Consistency problems for
Lévy Processes and Stochastic Calculus
Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random
Polynomial processes and their applications to mathematical finance
We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains
Polynomial diffusions and applications in finance
This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest
Levy processes and stochastic integrals in Banach spaces
We review in¯nite divisibility and Levy processes in Banach spaces and discuss the relationship with notions of type and cotype. The Levy-It^o decomposition is described. Strong, weak and
Introduction to stochastic partial differential equations
We introduce the Hilbert space-valued Wiener process and the corresponding stochastic integral of Ito type. This is then used together with semigroup theory to obtain existence and uniqueness of weak
The Heston stochastic volatility model in Hilbert space
ABSTRACT We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued
The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes
Abstract.  The Pearson diffusions form a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit