# Independent increment processes: a multilinearity preserving property

@article{Benth2018IndependentIP, title={Independent increment processes: a multilinearity preserving property}, author={Fred Espen Benth and Nils Detering and Paul Kr{\"u}hner}, journal={Stochastics}, year={2018}, volume={93}, pages={803 - 832} }

ABSTRACT We observe a multilinearity preserving property of conditional expectation for infinite-dimensional independent increment processes defined on some abstract Banach space B. It is similar in nature to the polynomial preserving property analysed greatly for finite-dimensional stochastic processes and thus offers an infinite-dimensional generalization. However, while polynomials are defined using the multiplication operator and as such require a Banach algebra structure, the…

## 3 Citations

### Abstract polynomial processes.

- Mathematics
- 2020

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 polynomial processes

- MathematicsFinance and Stochastics
- 2019

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…

## References

SHOWING 1-10 OF 21 REFERENCES

### Probability measure-valued polynomial diffusions

- MathematicsElectronic Journal of Probability
- 2019

We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional…

### Representation of Infinite-Dimensional Forward Price Models in Commodity Markets

- Mathematics
- 2014

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…

### Ornstein-Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility

- Mathematics
- 2015

### Levy processes and stochastic integrals in Banach spaces

- Mathematics
- 2007

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…

### Polynomial processes and their applications to mathematical finance

- MathematicsFinance Stochastics
- 2012

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…

### The Heston stochastic volatility model in Hilbert space

- Mathematics
- 2017

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…

### Polynomial diffusions and applications in finance

- MathematicsFinance Stochastics
- 2016

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…

### The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes

- Mathematics
- 2007

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…

### Space-time fractional stochastic partial differential equations with Lévy noise

- Mathematics
- 2019

Abstract We consider non-linear time-fractional stochastic heat type equation ∂βu∂tβ+ν(−Δ)α/2u=It1−β[∫Rdσ(u(t,x),h)N~⋅(t,x,h)]$$\begin{array}{} \displaystyle \frac{\partial^\beta u}{\partial…

### Consistency Problems for Heath-Jarrow-Morton Interest Rate Models (Lecture Notes in Mathematics 1760)

- Psychology
- 2001

Research monograph providing appropriate consistency conditions for and examples of blended models for the term structure of interest rates within the Health-Jarrow-Morton framework, combining…