{
  "annotation_id": "d89a036e-5607-4bcd-bf26-253d98ebf92c",
  "date_created": "2026-02-17T05:53:23.983000Z",
  "date_modified": "2026-02-17T05:53:23.983000Z",
  "file_hash": "eb476814bd7ef7f93d9792db72ed06fb0f481b614d5d71215ff6eab6b601956b",
  "private": false,
  "record": {
    "abstract": "We derive an It\\^o-type change-of-variables formula for a class of adapted stochastic processes that do not necessarily admit semimartingale structure. The formulation is based on an intrinsic Hilbert-space derivative together with a predictable projection operator, allowing stochastic integrals to be expressed without reliance on quadratic variation or anticipative calculus.\n  The resulting formula replaces the classical quadratic variation term with a computable second-order contribution expressed as a norm of the projected derivative. In the semimartingale case, the formula reduces to the classical It\\^o formula. The approach applies naturally to processes with memory and non-Markovian dependence, providing a unified and intrinsic framework for stochastic calculus beyond the semimartingale setting.",
    "arxiv_id": "2601.10359",
    "authors": [
      "Ramiro Fontes"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "An It\\^o Formula via Predictable Projection for Non-Semimartingale Processes",
    "url": "https://arxiv.org/abs/2601.10359",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6d22d166-c734-4c0f-9719-056870455f90",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}