Pith Number

pith:P2NGOCM7

pith:2025:P2NGOCM7THP2DPHS7IIMYFEZ5Q

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$L^{\alpha-1}$ distance between two one-dimensional stochastic differential equations with drift terms driven by a symmetric $\alpha$-stable process

Takuya Nakagawa

The L^{α-1} distance between solutions of one-dimensional α-stable SDEs with drifts satisfies a Hölder-type bound controlled by initial differences and a weighted coefficient norm.

arxiv:2510.25151 v3 · 2025-10-29 · math.PR

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\pithnumber{P2NGOCM7THP2DPHS7IIMYFEZ5Q}

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The main result is a Hölder-type estimate for the L^{α-1}(Ω) distance between two solution paths, which quantifies the stability with respect to the initial values and coefficients.

C2weakest assumption

The transition probability density of the baseline solution exists and can be used to construct a weighted integral norm that effectively localizes the error analysis for time-dependent coefficient perturbations.

C3one line summary

Establishes Hölder estimates for the L^{α-1} distance between solutions of 1D SDEs with symmetric α-stable drivers and drifts, via a weighted norm on coefficient perturbations and mollified auxiliary functions.

Receipt and verification

First computed	2026-06-02T03:04:35.363903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e9a67099f99dfa1bcf2fa10cc1499ec25eefa31d71f271cb3d01e0d8eb3bdf3

Aliases

arxiv: 2510.25151 · arxiv_version: 2510.25151v3 · doi: 10.48550/arxiv.2510.25151 · pith_short_12: P2NGOCM7THP2 · pith_short_16: P2NGOCM7THP2DPHS · pith_short_8: P2NGOCM7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/P2NGOCM7THP2DPHS7IIMYFEZ5Q \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7e9a67099f99dfa1bcf2fa10cc1499ec25eefa31d71f271cb3d01e0d8eb3bdf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae775fa9866572b06c72ee6c884f9c18471dd5c2f0b06d4687ac4ace4b0f5e19",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-10-29T04:08:27Z",
    "title_canon_sha256": "76b4a37e85a8a71d93cb12e06eb61a78eb26082125ff2daccac1745643e7192e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.25151",
    "kind": "arxiv",
    "version": 3
  }
}