# Levy processes and stochastic integrals in Banach spaces

@inproceedings{Applebaum2007LevyPA, title={Levy processes and stochastic integrals in Banach spaces}, author={David Applebaum}, year={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 Pettis-style notions of stochastic integral are introduced and applied to construct
generalised Ornstein-Uhlenbeck processes.

## 34 Citations

### Maximal Inequalities of the Itô Integral with Respect to Poisson Random Measures or Lévy Processes on Banach Spaces

- Mathematics
- 2011

We are interested in maximal inequalities satisfied by a stochastic integral driven by a Poisson random measure in a general Banach space.

### Martingales and stochastic calculus in Banach spaces

- Mathematics
- 2019

In this thesis we study martingales and stochastic integration of processes with values in UMD Banach spaces.

### Stochastic Reaction-diffusion Equations Driven by Jump Processes

- Mathematics
- 2018

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise,…

### The Itô integral for a certain class of Lévy processes and its application to stochastic partial differential equations

- Mathematics
- 2010

Stochastic integration with respect to a Wiener process in Banach spaces have been considered by several authors (Brzeźniak [5], Dettweiler [13], Neidhart [22] and Van Neerven, Veraar and Weiss…

### Law equivalence of Ornstein–Uhlenbeck processes driven by a Lévy process

- MathematicsIndagationes Mathematicae
- 2019

### Local characteristics and tangency of vector-valued martingales

- MathematicsProbability Surveys
- 2020

This paper is devoted to tangent martingales in Banach spaces. We provide the definition of tangency through local characteristics, basic $L^p$- and $\phi$-estimates, a precise construction of a…

### Itô isomorphisms for $L^{p}$-valued Poisson stochastic integrals

- Mathematics
- 2014

Motivated by the study of existence, uniqueness and regularity of solutions to stochastic partial differential equations driven by jump noise, we prove It\^{o} isomorphisms for $L^p$-valued…

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