Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 52 min ago
PreprintCC BY 4.0arXiv

Monotone Mixing and Distribution Dynamics

  • Takashi Kamihigashi
  • Qingyin Ma
  • John Stachurski
Open at sourcePDFDOICite

Abstract

Many economic applications establish stability of Markov dynamics using the monotone mixing condition (MMC) of Hopenhayn and Prescott (1992). Working in the same setting as that paper, we introduce a weak monotone mixing condition (WMMC), phrased in terms of the reversal of rank between populations, and show that it is strictly weaker than the MMC and both necessary and sufficient for global stability under the Kolmogorov metric. We apply these results to a small open economy version of the Aiyagari model, showing how the WMMC can be used to establish global stability in a setting where the MMC fails. In addition, we show that, when the state space is one-dimensional, the MMC and WMMC coincide, implying that the original MMC is necessary as well as sufficient in this setting.

Related

  1. Mixing time under monotone censoring
    Yiming Chen, Yuval Peres
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  2. On Fixed-Time Stability of Continuous Dynamics for Non-Monotone Variational Inequalities
    Sina Arefizadeh, Kunal Garg, Angelia Nedić
    arXivPreprintarXiv licenceFull textDynamical systemsOptimisation & controlarXiv
  3. Consensus times for monotone aggregation dynamics
    Elchanan Mossel
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Non-autonomous dynamics of inner functions: mixing and entropy
    Vasiliki Evdoridou, Núria Fagella, Philip Rippon +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsDynamical systemsarXiv
  5. Mixing zone dynamics for the Saffman-Taylor instability with viscosity jump
    Paula Luna-Velasco, Francisco Mengual
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{kamihigashi2026monotone,
  title = {{Monotone Mixing and Distribution Dynamics}},
  author = {Takashi Kamihigashi and Qingyin Ma and John Stachurski},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33900},
  eprint = {2609.33900},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33900},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Monotone Mixing and Distribution Dynamics
AU  - Takashi Kamihigashi
AU  - Qingyin Ma
AU  - John Stachurski
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33900
UR  - https://arxiv.org/abs/2609.33900
AB  - Many economic applications establish stability of Markov dynamics using the monotone mixing condition (MMC) of Hopenhayn and Prescott (1992). Working in the same setting as that paper, we introduce a weak monotone mixing condition (WMMC), phrased in terms of the reversal of rank between populations, and show that it is strictly weaker than the MMC and both necessary and sufficient for global stability under the Kolmogorov metric. We apply these results to a small open economy version of the Aiyagari model, showing how the WMMC can be used to establish global stability in a setting where the MMC fails. In addition, we show that, when the state space is one-dimensional, the MMC and WMMC coincide, implying that the original MMC is necessary as well as sufficient in this setting.
ER  -