{
  "abstract": "Consider a random walk Sn = n i=1 Xi with independent and identically distributed real-valued increments with zero mean, finite variance and moment of order 2 + δ for some δ > 0. For any starting point x ∈ R, let τx = inf {k ⩾ 1 : x + S k < 0} denote the first time when the random walk x+Sn exits the half-line [0, ∞). We investigate the uniform asymptotic behavior over x ∈ R of the persistence probability P(τx > n) and the joint distribution P (x + Sn ⩽ u, τx > n), for u ⩾ 0, as n → ∞. New limit theorems for these probabilities are established based on the heat kernel approximations. Additionally, we evaluate the rate of convergence by proving Berry-Esseen type bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2412.08932",
  "author_total": 2,
  "authors": [
    {
      "name": "Ion Grama"
    },
    {
      "name": "Hui Xiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ek6nfcjt0h0yh.bib",
  "cited_by": 0,
  "doi": "10.1016/j.spa.2026.105113",
  "fulltext_url": null,
  "id": "ek6nfcjt0h0yh",
  "issns": [
    "0304-4149",
    "1879-209X"
  ],
  "landing_url": "https://hal.science/hal-05848310v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W4405354794",
  "pdf_url": "https://hal.science/hal-05848310/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/ek6nfcjt0h0yh.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:17Z",
      "native_id": "hal-05848310",
      "source": "hal",
      "url": "https://hal.science/hal-05848310v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Gaussian heat kernel asymptotics for conditioned random walks",
  "title_text": "Gaussian heat kernel asymptotics for conditioned random walks",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T12:20:48Z",
  "url": "https://research.draconitic.com/paper/ek6nfcjt0h0yh",
  "venue": "Stochastic Processes and their Applications",
  "versions": []
}