{
  "abstract": "We investigate the fake stationarity properties of solutions to forward Stochastic Volterra Integral Equations (SVIEs) with affine drift and long-memory (regular) kernels, both on finite horizons and in the long-run regime. By either deriving explicit closed-form specifications for the deterministic initial condition ϕ and the mean-reversion function µ appearing in the drift, or by introducing a deterministic stabilizing factor ς in the diffusion coefficient associated with the kernel while keeping µ fully flexible, we show that it is possible to induce a fake stationary regime, in the sense that all marginal distributions share the same mean and variance. Afterwards, using a refined asymptotic analysis, we further establish that, in both frameworks, the time-shifted solutions of these long-memory SVIEs converge weakly, in the functional sense, toward a family of L 2 -stationary processes sharing the same covariance structure, for suitable classes of diffusion coefficients. These results are applied to a class of exponential-fractional Stochastic Volterra Integral Equations driven by an α-gamma fractional integration kernel, in the particular regime α ≥ 1, which regularizes diffusion paths and invoke long-term memory, persistence or long range dependence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.31099",
  "author_total": 2,
  "authors": [
    {
      "name": "Emmanuel Gnabeyeu"
    },
    {
      "name": "Gilles Pagès"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3kgtpt3yj87fs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.31099",
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  "id": "3kgtpt3yj87fs",
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  "language": "en",
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  "pdf_url": "https://hal.science/hal-05733278/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3kgtpt3yj87fs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:24Z",
      "native_id": "hal-05733278",
      "source": "hal",
      "url": "https://hal.science/hal-05733278v1"
    },
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.31099",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.31099"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels",
  "title_text": "On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/3kgtpt3yj87fs",
  "venue": "HAL",
  "versions": []
}