Stochastic integration in Banach spaces - a survey

2013/04/29 by van Neerven, Jan, Veraar, Mark, Weis, Lutz · 2 citations
#46E40 #60H15 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 60H05 #Probability (math.PR) #Secondary: 46B09

paper · doi:10.48550/arxiv.1304.7575

Abstract

This paper presents a brief survey of the theory of stochastic integration in Banach spaces. Expositions of the stochastic integrals in martingale type 2 spaces and UMD spaces are presented, as well as some applications of the latter to vector-valued Malliavin calculus and the stochastic maximal regularity problem. A new proof of the stochastic maximal regularity theorem is included.

Cited by

• A stochastic flow approach to De Giorgi-Nash-Moser estimates for SPDEs with smooth transport noise
• Functional calculus on weighted Sobolev spaces for the Laplacian on rough domains

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