Stochastic integration in UMD Banach spaces

• 成果类型: Article
• 署名作者: van Neerven, J. M. A. M.; Veraar, M. C.; Weis, L.
• 署名单位: Delft University of Technology; Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000001006
• 发表日期: 2007
• 页码: 1438-1478
• 关键词: values; martingales

摘要

In this paper we construct a theory of stochastic integration of processes with values in L(H, E), where H is a separable Hilbert space and E is a UMD Banach space (i.e., a space in which martingale differences are unconditional). The integrator is an H-cylindrical Brownian motion. Our approach is based on a two-sided L-p-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of L(H, E)-valued functions introduced recently by two of the authors. We obtain various characterizations of the stochastic integral and prove versions of the Ito isometry, the Burkholder-Davis-Gundy inequalities, and the representation theorem for Brownian martingales.