{
  "titles": [
    {
      "title": "Non-commutative $L^{p}$ spaces and Grassmann stochastic analysis"
    }
  ],
  "creators": [
    {
      "name": "De Vecchi, Francesco C.",
      "nameType": "Personal",
      "familyName": "De Vecchi",
      "givenName": "Francesco C."
    },
    {
      "name": "Fresta, Luca",
      "nameType": "Personal",
      "familyName": "Fresta",
      "givenName": "Luca"
    },
    {
      "name": "Gordina, Maria",
      "nameType": "Personal",
      "familyName": "Gordina",
      "givenName": "Maria"
    },
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2023,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "1",
  "url": "https://arxiv.org/abs/2305.08497v1",
  "dates": [
    {
      "date": "2023-05-15",
      "dateType": "Issued"
    },
    {
      "date": "2023-05-15",
      "dateType": "Available"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-texmacs"
  ],
  "subjects": [
    {
      "subject": "math.PR",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math-ph",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.MP",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.OA",
      "subjectScheme": "arXiv"
    }
  ],
  "rightsList": [
    {
      "rights": "arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors",
      "rightsUri": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
    }
  ],
  "descriptions": [
    {
      "description": "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 Itô 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 $\\Phi^{4}_{2}$.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:2305.08497v1",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.2305.08497",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    }
  ]
}