Pith Number

pith:VRDMESBD

pith:2026:VRDMESBDL7D4IGNJ2MBJNC3PCZ

not attested not anchored not stored refs resolved

Geometric Brownian motion with intermittent entries and exits

Arnab Pal, Suvam Pal, Trifce Sandev, Viktor Stojkoski

Geometric Brownian motion with unequal entry and exit rates still reaches a stationary distribution, and an optimal exit rate minimizes the mean time to hit a threshold.

arxiv:2605.17299 v1 · 2026-05-17 · econ.GN · q-fin.EC · q-fin.RM

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\usepackage{pith}
\pithnumber{VRDMESBDL7D4IGNJ2MBJNC3PCZ}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Despite the asymmetry in the entry and exit rates, the system eventually relaxes to a stationary distribution; moreover, there exists an optimal exit rate that minimizes the mean first-passage time to a threshold.

C2weakest assumption

The entry and exit events are treated as independent Poisson processes whose rates do not depend on the current state of the geometric Brownian motion variable itself (section on model definition and the derivation of the stationary distribution).

C3one line summary

A generalized geometric Brownian motion with independent entry and exit rates relaxes to a stationary distribution, exhibits three moment regimes, and has an optimal exit rate minimizing mean first-passage time.

References

61 extracted · 61 resolved · 1 Pith anchors

[1] S. Redner, Am. J. Phys.58, 267 (1990) 1990

[2] F. Black and M. Scholes, J. Polit. Econ.81, 637 (1973) 1973

[3] R. C. Merton, J. Finance29, 449 (1974) 1974

[4] J. Aitchison and J. A. C. Brown, Metroeconomica6, 88 (1954) 1954

[5] X. Gabaix, J.-M. Lasry, P.-L. Lions, and B. Moll, Econometrica84, 2071 (2016) 2071

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:50.966433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac46c248235fc7c419a9d302968b6f165d2365fc3782c1da16981d2f6502b164

Aliases

arxiv: 2605.17299 · arxiv_version: 2605.17299v1 · doi: 10.48550/arxiv.2605.17299 · pith_short_12: VRDMESBDL7D4 · pith_short_16: VRDMESBDL7D4IGNJ · pith_short_8: VRDMESBD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VRDMESBDL7D4IGNJ2MBJNC3PCZ \
  | 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: ac46c248235fc7c419a9d302968b6f165d2365fc3782c1da16981d2f6502b164

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8fe034e18156047bd10ca5c06eed248b315591a97d746cd9c08cace34dfc5fb",
    "cross_cats_sorted": [
      "q-fin.EC",
      "q-fin.RM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "econ.GN",
    "submitted_at": "2026-05-17T07:20:30Z",
    "title_canon_sha256": "318d51c05b2e278b7278d9ad1a85684506867d5b045f14e7c6c7cf3533d8c0a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17299",
    "kind": "arxiv",
    "version": 1
  }
}