Pith Number

pith:GRYEKNMJ

pith:2026:GRYEKNMJNRUSJ3G5YCDMN73WTD

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Sticky CIR process with potential: invariant measure and exact sampling

Tony Shardlow

For δ in (1,2), the sticky CIR process is well-posed and possesses a unique invariant measure that mixes a point mass at zero with a weighted gamma-type density on the interior.

arxiv:2605.13648 v1 · 2026-05-13 · math.PR · cs.NA · math.NA

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Claims

C1strongest claim

For the parameter range δ∈(1,2), in which the origin is accessible but not absorbing, we prove well-posedness of the process and uniqueness of its invariant measure, which is a mixture of a point mass at zero and a weighted gamma-type density on the interior. We derive an explicit Green's function for the resolvent in terms of confluent hypergeometric functions, and use this to construct an exact sampler for the invariant measure in the zero-potential case.

C2weakest assumption

The Girsanov change of measure correctly tilts the invariant distribution for non-trivial potential G while preserving the sticky boundary behavior; the parameter range δ∈(1,2) ensures the origin is accessible but not absorbing without additional regularity conditions on the potential.

C3one line summary

Proves well-posedness and unique invariant measure for the sticky CIR process and constructs exact and approximate samplers using Green's functions and Girsanov change of measure.

References

14 extracted · 14 resolved · 1 Pith anchors

[1] and Salminen, Paavo , TITLE = 2002 · doi:10.1007/978-3-0348-8163-0

[2] Hadamard Langevin dynamics for sampling the l1-prior 2026 · doi:10.48550/arxiv.2411.11403

[3] COX, J. C., INGERSOLL, J. E. and ROSS, S. A. (1985). A Theory of the Term Structure of Interest Rates. Econometrica53385–407. https://doi.org/10.2307/1911242 1985 · doi:10.2307/1911242

[4] Journal of the American Statistical Association , author = 1993 · doi:10.1080/01621459.1993.10476353

[5] HAIRER, M. and MATTINGLY, J. C. (2011). Yet another look at Harris’ ergodic theorem for Markov chains. InSeminar on Stochastic Analysis, Random Fields and Applications VI.Progress in Probability63109– 2011 · doi:10.1007/978-3-0348-0021-1_7

Receipt and verification

First computed	2026-05-18T02:44:17.508343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34704535896c6924ecddc086c6ff7698ccb9bb7d746c568b0320aacd2348632d

Aliases

arxiv: 2605.13648 · arxiv_version: 2605.13648v1 · doi: 10.48550/arxiv.2605.13648 · pith_short_12: GRYEKNMJNRUS · pith_short_16: GRYEKNMJNRUSJ3G5 · pith_short_8: GRYEKNMJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GRYEKNMJNRUSJ3G5YCDMN73WTD \
  | 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: 34704535896c6924ecddc086c6ff7698ccb9bb7d746c568b0320aacd2348632d

Canonical record JSON

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    "abstract_canon_sha256": "da8c406154e9aded965124e2ebf1c3e015256a60262ef9b3f12b24edbc677e74",
    "cross_cats_sorted": [
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    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-13T15:07:10Z",
    "title_canon_sha256": "dfad74803544bd550d0bca77dc3f39af38def8163a6c2be6d2061c6ded6e1791"
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