{
  "annotation_id": "6ff42c83-4d4c-4f39-98d8-32ec1abbba09",
  "date_created": "2026-02-17T05:53:08.113000Z",
  "date_modified": "2026-02-17T05:53:08.113000Z",
  "file_hash": "abd149f682196208d79774dc61f38927b63cd4c3281da64f5c3cba19898a6dc1",
  "private": false,
  "record": {
    "abstract": "This paper introduces a variable-order stable subordinator (VOSS) $S^{\\alpha(t)}(t)$ with index $\\alpha(t)\\in(0,1)$, where $\\alpha(t)$ is a right-continuous piecewise constant function. We drive the Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator (GSFPP-VO) defined by $\\{N(S^{\\alpha(t)}(t))\\}_{t \\geq 0}$, obtained by time-changing a homogeneous Poisson process $\\{N(t,\\lambda)\\}_{t\\geq 0}$ with rate parameter $\\lambda\u003e0$ by an independent VOSS. Explicit expressions for the Laplace transform, probability generating function, probability mass function, and moment generating function of the GSFPP-VO are derived, and these quantities are shown to satisfy partial differential equations. Finally, we establish the associated generalized distributions, analyze the hitting-time properties, and characterize the L\\\u0027evy measures of the GSFPP-VO.",
    "arxiv_id": "2601.06808",
    "authors": [
      "Reetendra Singh",
      "Aditya Maheshwari"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "title": "Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator",
    "url": "https://arxiv.org/abs/2601.06808",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "75c91216-9b8e-4a81-9c0c-93bca15b0ba5",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}