scholarly journals Stochastic Integration in Banach Spaces – a Survey

2015 ◽  
pp. 297-332 ◽  
Author(s):  
Jan van Neerven ◽  
Mark Veraar ◽  
Lutz Weis
Keyword(s):  
Banach Spaces ◽  
Stochastic Integration

scholarly journals Stochastic integration in UMD Banach spaces

2007 ◽  
Vol 35 (4) ◽  
pp. 1438-1478 ◽  
Author(s):  
J. M. A. M. van Neerven ◽  
M. C. Veraar ◽  
L. Weis
Keyword(s):  
Banach Spaces ◽  
Stochastic Integration ◽  
Umd Banach Spaces

Vector Integration and Stochastic Integration in Banach Spaces

2018 ◽  
Author(s):  
Nicolae Dinculeanu
Keyword(s):  
Banach Spaces ◽  
Positive Measure ◽  
Integration Theory ◽  
Stochastic Integration ◽  
Bochner Integral ◽  
Finite Variation ◽  
Vector Measures ◽  
Vector Integration ◽  
Step Functions ◽  
Integrable Variation

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 and its applications. This theory reduces to integration with respect to vector measures with finite variation which, in turn, reduces to the Bochner integral with respect to a positive measure. The article describes the four stages in the development of integration theory. It first provides an overview of the relevant notation for Banach spaces, measurable functions, the integral of step functions, and measurability with respect to a positive measure before discussing the Bochner integral. It then examines integration with respect to measures with finite variation, semivariation of vector measures, integration with respect to a measure with finite semivariation, and stochastic integrals. It also reviews processes with integrable variation or integrable semivariation and concludes with an analysis of martingales.

scholarly journals Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators

2020 ◽  
Author(s):  
Tomasz Kosmala ◽  
Markus Riedle
Keyword(s):  
Evolution Equation ◽  
Banach Spaces ◽  
Lévy Processes ◽  
Stochastic Integral ◽  
Levy Processes ◽  
Integration Theory ◽  
Stochastic Evolution Equation ◽  
Stochastic Integration ◽  
Stochastic Evolution ◽  
Existence Of A Solution

AbstractWe introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for $$p\in [1,2]$$p∈[1,2]. The space of integrands consists of p-summing operators between Banach spaces of martingale type p. We apply the developed integration theory to establish the existence of a solution for a stochastic evolution equation driven by a cylindrical Lévy process.

Stochastic Integration in Banach Spaces

1991 ◽  
pp. 27-115 ◽  
Author(s):  
J. K. Brooks ◽  
N. Dinculeanu
Keyword(s):  
Banach Spaces ◽  
Stochastic Integration

An Approach to Stochastic Integration in General Separable Banach Spaces

2018 ◽  
Vol 50 (4) ◽  
pp. 591-608
Author(s):  
A. A. Kalinichenko
Keyword(s):  
Banach Spaces ◽  
Stochastic Integration
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