Non-commutative Lp spaces and Grassmann stochastic analysis

• 成果类型: Article
• 署名作者: De Vecchi, Francesco; Fresta, Luca; Gordina, Maria; Gubinelli, Massimiliano
• 署名单位: University of Pavia; Roma Tre University; University of Connecticut; University of Oxford
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01379-4
• 发表日期: 2025
• 页码: 949-1029
• 关键词: quantization; ALGEBRAS; PROPERTY

摘要

We introduce a theory of non-commutative L-p spaces suitable for non-commutative probability in a non-tracial setting and use it to develop stochastic analysis of Grassmann-valued processes, including martingale inequalities, stochastic integrals with respect to Ito-Grassmann processes, Girsanov's formula and a weak formulation of Grassmann SDEs. We apply this new setting to the construction of several unbounded random variables including a Grassmann analog of the Phi(2)(4) Euclidean QFT in a bounded region and weak solution to singular SPDEs in the spirit of the early work of Jona-Lasinio and Mitter on the stochastic quantisation of Phi(2)(4)\.