Non-commutative $L^{p}$ spaces and Grassmann stochastic analysis

Autor:	De Vecchi, Francesco C., Fresta, Luca, Gordina, Maria, Gubinelli, Massimiliano
Rok vydání:	2023
Předmět:	Mathematics - Probability Mathematical Physics Mathematics - Operator Algebras
Druh dokumentu:	Working Paper
Popis:	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 Grassmann It\^o 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 $\Phi^{4}_{2}$ 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 $\Phi^{4}_{2}$. Comment: 59 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.08497 Zobrazit plný text záznamu View this record from Arxiv