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pith:MKKRT7UT

pith:2026:MKKRT7UTTZD6XELYKTH34LF5HV

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Stopping Times in the Filtration of a Brownian Motion Stopped at its Last Passage Time

Mohammed Louriki

The last passage time of Brownian motion with positive drift is the unique totally inaccessible stopping time in the filtration of the stopped process.

arxiv:2605.14254 v1 · 2026-05-14 · math.PR

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Claims

C1strongest claim

We compute the compensator of σ_z^λ and establish that it is the unique totally inaccessible stopping time in the filtration of ξ^λ,z. Moreover, for any stopping time T, the restriction of T to {T = σ_z^λ} is totally inaccessible, while its restriction to {T ≠ σ_z^λ} is predictable.

C2weakest assumption

The analysis assumes the standard construction of Brownian motion with positive drift λ > 0 and the usual augmentation of the natural filtration generated by the stopped process ξ^λ,z; no additional regularity beyond continuity of paths is postulated.

C3one line summary

The last passage time of a drifted Brownian motion is the unique totally inaccessible stopping time in its stopped filtration; the extended process with an indicator of whether time is before the passage is Feller.

References

52 extracted · 52 resolved · 0 Pith anchors

[1] Abramowitz, M; Stegun I.A.Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York, 1992 1992

[2] SpringerBriefs in Quantitative Finance 2017

[3] Integral representations of martingales for progres- sive enlargements of filtrations 2019

[4] On the distribution of the maximum of a Gaussian field withd parameters 2005

[5] L.; Buckdahn, R.; Engelbert, H 2017

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:10.541633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

629519fe939e47eb917854cfbe2cbd3d6e9152880e84a8366b4ffb54daeac34e

Aliases

arxiv: 2605.14254 · arxiv_version: 2605.14254v1 · doi: 10.48550/arxiv.2605.14254 · pith_short_12: MKKRT7UTTZD6 · pith_short_16: MKKRT7UTTZD6XELY · pith_short_8: MKKRT7UT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MKKRT7UTTZD6XELYKTH34LF5HV \
  | 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: 629519fe939e47eb917854cfbe2cbd3d6e9152880e84a8366b4ffb54daeac34e

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-14T01:47:48Z",
    "title_canon_sha256": "56c0e6b6602ca769c57c98e06bc451143783c311ee70afced4c76e6f031ca6cc"
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