Pith Number

pith:A7BN56AI

pith:2025:A7BN56AII6B3PWYNUOU6K25LZU

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Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes

Th\'eo Leblanc

A Hawkes autoregressive model merges continuous Hawkes dynamics with discrete autoregressive ones to handle multiscale heterogeneous data.

arxiv:2511.10132 v2 · 2025-11-13 · math.ST · math.ST · stat.TH

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Record completeness

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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

we introduce this new Hawkes autoregressive (HAR) model incorporating both continuous- and discrete-time dynamics, and establish several probabilistic results, including the existence of a stationary version, a cluster representation, as well as stability and ergodic properties.

C2weakest assumption

The combined Hawkes and autoregressive dynamics can be defined on a common probability space without internal contradictions that would prevent the claimed stationary version or cluster representation from existing.

C3one line summary

A new Hawkes autoregressive process combines Hawkes and autoregressive dynamics, with proofs of a stationary version, cluster representation, stability, and ergodicity.

References

60 extracted · 60 resolved · 0 Pith anchors

[1] AMORINO, C., DION-BLANC, C., GLOTER, A. and LEMLER, S. (2025). Nonparametric estimation of the stationary density for Hawkes-diffusion systems with known and unknown intensity. arXiv:2412.08386 [math] 2025 · doi:10.48550/arxiv.2412.08386

[2] BACRY, E., BOMPAIRE, M., GAÏFFAS, S. and MUZY, J.-F. (2020). Sparse and low-rank multivariate Hawkes processes.Journal of Machine Learning Research211–32 2020

[3] BACRY, E., DELATTRE, S., HOFFMANN, M. and MUZY, J. F. (2013). Some limit theorems for Hawkes processes and application to financial statistics.Stochastic Processes and their Applications1232475–2499. 2013 · doi:10.1016/j.spa.2013.04.007

[4] Quantifying grid resilience against extreme weather using large-scale customer power outage data, 2027 · doi:10.5705/ss.202023.0017

[5] BASSEVILLE, M., BENVENISTE, A. and WILLSKY, A. (1992). Multiscale Autoregressive Processes, Part I: Schur-Levinson Parametrizations. Signal Processing, IEEE Transactions on401915–1934. https://doi.org 1992 · doi:10.1109/78.149995

Formal links

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Receipt and verification

First computed	2026-05-28T13:04:47.334730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07c2def8084783b7db0da3a9e56babcd34b18524ef373fa6889d02bfead21b22

Aliases

arxiv: 2511.10132 · arxiv_version: 2511.10132v2 · doi: 10.48550/arxiv.2511.10132 · pith_short_12: A7BN56AII6B3 · pith_short_16: A7BN56AII6B3PWYN · pith_short_8: A7BN56AI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/A7BN56AII6B3PWYNUOU6K25LZU \
  | 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: 07c2def8084783b7db0da3a9e56babcd34b18524ef373fa6889d02bfead21b22

Canonical record JSON

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    "abstract_canon_sha256": "1472a5ff9cd93b36a05792b012d6d5514f9d88c12fbdaa2f3ab20ea20ee1347f",
    "cross_cats_sorted": [
      "math.ST",
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    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2025-11-13T09:38:56Z",
    "title_canon_sha256": "fb288d63dc35c6bc53bd7a0c9ff0224187d5905cd001a4b0049d3507898e3cec"
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