{
  "abstract": "Additive functionals $\\overline{J}_t=\\frac{1}{t}\\int_0^tU(X_s)\\circ dX_s$ of Stratonovich-type recently attracted much attention in the context of inference of thermodynamic properties of complex systems from observations $U$ of individual fluctuating paths $(X_s)_{0\\le s\\le t}$, whereby $X_0$ is initiated from some general measure. Concentration results on $\\overline{J}_t$, albeit desirable, are virtually nonexistent. They turn out to be significantly more challenging to prove than for classical Lebesgue-type functionals $\\overlineρ_t=\\frac{1}{t}\\int_0^t V(X_s)ds$ because the tilt deforms the full second-order structure of the Feynman-Kac generator instead of contributing an additive potential. This renders the generator generally non-self-adjoint even under detailed balance. We overcome this by working with a symmetrized Dirichlet form with a new effective potential that now couples the observable to the non-equilibrium character of the dynamics. We prove concentration inequalities for $\\overline{J}_t$ for any bounded, sufficiently smooth vector-valued function $U$ of a general geometrically ergodic diffusion process $X_s$, including explicit sub-gamma and Bernstein-type inequalities, and we obtain explicit upper bounds on ${\\rm Var}(\\overline{J}_t)$. Strikingly, under detailed balance the concentration of $\\overline{J}_t$ is distinctively sub-Gaussian at all times and all deviations, with a variance proxy fixed by the noise alone and independent of the spectral gap, which has no analog for $\\overlineρ_t$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01581",
  "author_total": 3,
  "authors": [
    {
      "name": "Rick Bebon"
    },
    {
      "name": "Aljaž Godec"
    },
    {
      "name": "Angelika Rohde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5fng7wsr8gz96.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01581",
  "fulltext_url": null,
  "id": "5fng7wsr8gz96",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01581",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7206167133",
  "pdf_url": "https://arxiv.org/pdf/2609.01581",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5fng7wsr8gz96.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.01581",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01581"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Concentration of additive functionals of Stratonovich-type",
  "title_text": "Concentration of additive functionals of Stratonovich-type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/5fng7wsr8gz96",
  "venue": "arXiv",
  "versions": []
}