Stochastic Integration in Banach Spaces using a product structure with partial order

2009/10/28 by Joris Bierkens, Bierkens, Joris, Onno van Gaans +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60H05 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0910.5363

openalex publication_date 2009/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales.

Related

• Stochastic integration in Banach spaces - a survey
• Conditions for stochastic integrability in UMD Banach spaces
• Poisson stochastic integration in Banach spaces
• The martingale representation theorem for cylindrical martingale valued measures
• Stochastic integration with respect to arbitrary collections of continuous semimartingales and applications to Mathematical Finance