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pith:RSVGOWY5

pith:2026:RSVGOWY5ZLSHVB2L3I5OU35Z2W

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Stochastic Mackey-Glass Equations and Other Negative Feedback Systems: Existence of Invariant Measures

Mark van den Bosch, Onno van Gaans, Sjoerd Verduyn Lunel

Non-trivial invariant measures exist for stochastic negative feedback systems if and only if solutions from at least one initial condition remain bounded away from zero in probability.

arxiv:2605.14134 v1 · 2026-05-13 · math.DS · math.PR

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Claims

C1strongest claim

A non-trivial invariant measure is proved to exist if and only if there is at least one initial condition for which the solution remains bounded away from zero in probability.

C2weakest assumption

The mild assumptions ensuring global persistence and upper boundedness in probability for the stochastic negative feedback systems, together with the noise being a square integrable Lévy process with finite intensity.

C3one line summary

Non-trivial invariant measures exist for stochastic Mackey-Glass and Nicholson's blowflies equations if and only if solutions remain bounded away from zero in probability for at least one initial condition.

References

84 extracted · 84 resolved · 2 Pith anchors

[1] R. J. Adler and J. E. Taylor (2009). Random fields and geometry. Springer Science & Business Media 2009

[2] Applebaum (2009) 2009

[3] J. A. D. Appleby and E. Buckwar (2003). Noise induced oscillation in solutions of stochastic delay differential equations. Tech. rep. SFB 373 Discussion Paper 2003

[4] J. A. D. Appleby and C. Kelly (2004). Oscillation and non-oscillation in solutions of nonlinear stochastic delay differential equations. Electronic Communications in Probability 9, 106–118 2004

[5] J. Bao, G. Yin, and C. Yuan (2016). Asymptotic Analysis for Functional Stochastic Differential Equations. SpringerBriefs in Mathematics. Springer International Publishing 2016

Receipt and verification

First computed	2026-05-17T23:39:11.759472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8caa675b1dcae47a874bda3aea6fb9d5bbbaae943a6ccc02e38afaa4b1c5cc68

Aliases

arxiv: 2605.14134 · arxiv_version: 2605.14134v1 · doi: 10.48550/arxiv.2605.14134 · pith_short_12: RSVGOWY5ZLSH · pith_short_16: RSVGOWY5ZLSHVB2L · pith_short_8: RSVGOWY5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RSVGOWY5ZLSHVB2L3I5OU35Z2W \
  | 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: 8caa675b1dcae47a874bda3aea6fb9d5bbbaae943a6ccc02e38afaa4b1c5cc68

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "79cee809c050c43575722a22ff9778435270b8497b00aab722fce6e2599f8c1f",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-13T21:37:24Z",
    "title_canon_sha256": "770745163fca734f30bb1287e2cce1047bb1af6183a7cdecf9420996bc85e547"
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  "source": {
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    "kind": "arxiv",
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}