Stochastic integration for Lévy processes with values in Banach spaces
type: Item
instance of: scholarly article
title: Stochastic integration for Lévy processes with values in Banach spaces
zbMATH Open document ID: 1179.60033
author: M. Riedle
author: O. W. van Gaans
published in: Stochastic Processes and their Applications
publication date: 2009-06-04T00:00:00Z
full work available at URL: riedle-vangaans SPA 1405 rev2.pdf
review text: The aim of the authors is to define a stochastic integral with respect to a Banach space \(B\)-valued Lévy process \((L_t)\), and to use it, in order to get a Lévy-Itô decomposition (extending the classical finite-dimensional one) for \((L_t)\), and finally to solve Cauchy problems of type: \[ dY_t= AY_t dt+ \int H(u)\,dL_t, \] for some generator \(A\) and \(L^2\) function \(H\). These goals are achieved, essentially by considering systematically the weak version (with respect to the dual of \(B\)) of the above objects, and by restricting to deterministic Banach valued integrands.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 5561597
zbMATH Keywords: Banach space valued stochastic integral
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Lévy-Itô decomposition
zbMATH Keywords: Lévy process
zbMATH Keywords: martingale valued measure
zbMATH Keywords: Pettis integral
zbMATH Keywords: radonifying operator
MaRDI profile type: Publication
OpenAlex ID: W2103014316
cites work: Stochastic Integrals and the Lévy–Ito Decomposition Theorem on Separable Banach Spaces
cites work: Lévy Processes and Stochastic Calculus
cites work: Q5294262
cites work: Q5420976
cites work: Q3906818
cites work: On the small balls problem for equivalent Gaussian measures
cites work: Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem
cites work: Interest rate models: an infinite dimensional stochastic analysis perspective
cites work: Stochastic Equations in Infinite Dimensions
cites work: Q3660590
cites work: Q3041461
cites work: An Introduction to Banach Space Theory
cites work: Q5512462
cites work: Stochastic Partial Differential Equations with Levy Noise
cites work: Q3779530
cites work: On the space of vector-valued functions integrable with respect to the white noise
cites work: Stochastic integration of functions with values in a Banach space
cites work: Stochastic integration in UMD Banach spaces
cites work: Q4040351
cites work: Q3747436
cites work: Applied functional analysis. Applications to mathematical physics. Vol. 1
DOI: 10.1016/J.SPA.2008.09.009
description: scientific article; zbMATH DE number 5561597