Pith Number

pith:KU374JYA

pith:2026:KU374JYA7AJQQ6EJTGJBFC47XN

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Stochastic evolution equations driven by arbitrary cylindrical L\'evy processes

Adam Jakubowski, Gergely Bod\'o, Markus Riedle, Sonja Cox

Mild solutions exist and are unique for abstract stochastic evolution equations driven by arbitrary cylindrical Lévy processes in Hilbert spaces.

arxiv:2605.13727 v1 · 2026-05-13 · math.PR

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Claims

C1strongest claim

We establish the first existence and uniqueness result for mild solutions of abstract stochastic evolution equations driven by arbitrary cylindrical Lévy processes in Hilbert spaces.

C2weakest assumption

The coefficients satisfy global Lipschitz conditions and the pathwise adaptive Euler-Peano approximation scheme based on noise-dependent stopping times converges to a mild solution without any moment assumptions on the cylindrical Lévy process.

C3one line summary

Existence and uniqueness of mild solutions is established for stochastic evolution equations driven by arbitrary cylindrical Lévy processes under global Lipschitz conditions on the coefficients.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] Amann.Ordinary differential equations 1990

[2] D. Applebaum and M. Riedle. Cylindrical L´ evy processes in Banach spaces.Proc. Lond. Math. Soc. (3), 101(3):697–726, 2010 2010

[3] Bichteler.Stochastic integration with jumps 2002

[4] Bod´ o and M 2025

[5] G. Bod´ o, O. T´ ybl, and M. Riedle. SPDEs driven by standard symmetricα-stable cylindrical L´ evy processes: existence, Lyapunov functionals and Itˆ o formula.Elec- tron. J. Probab., 29:Paper No. 79, 2024

Receipt and verification

First computed	2026-05-18T02:44:16.597036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5537fe2700f8130878899992128b9fbb5ccda5bf034cfa2069232a819234dd4c

Aliases

arxiv: 2605.13727 · arxiv_version: 2605.13727v1 · doi: 10.48550/arxiv.2605.13727 · pith_short_12: KU374JYA7AJQ · pith_short_16: KU374JYA7AJQQ6EJ · pith_short_8: KU374JYA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KU374JYA7AJQQ6EJTGJBFC47XN \
  | 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: 5537fe2700f8130878899992128b9fbb5ccda5bf034cfa2069232a819234dd4c

Canonical record JSON

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    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-13T16:07:07Z",
    "title_canon_sha256": "3f28f0c75adccdf2082dd4e45951696500b2e509f5d51362b1f3402b51912611"
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    "kind": "arxiv",
    "version": 1
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}