Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 53 min ago
PreprintarXiv licencearXiv

Stability results for distribution-dependent stochastic Volterra equations

  • Martin Bergerhausen
  • David J. Prömel
Open at sourcePDFDOICite

Abstract

We investigate stability properties of distribution-dependent stochastic Volterra equations with respect to changes in the coefficients, the Volterra kernels, and the initial condition. Under Lipschitz continuity assumptions on the coefficients, we first derive quantitative stability estimates for strong solutions with explicit error bounds. We then prove a general convergence theorem for strong solutions under substantially weaker assumptions, replacing Lipschitz continuity by a continuity assumption together with uniform linear growth of the approximating sequence. Finally, we study the associated distribution-dependent Volterra local martingale problem and prove the stability of its solutions under convergence of the coefficients, kernels, and initial distributions.

Related

  1. Wong--Zakai Convergence and FNO Learning for Stochastic Volterra Equations
    Wonjae Lee, Jiuk Jang, Hyungbin Park
    arXivPreprintarXiv licenceFull textProbabilityStatisticsarXiv
  2. Convergence in Hölder norms for Markovian approximations of stochastic Volterra equations
    Noé Corneille, Kristin Kirchner, Pietro Pezzoli Frigerio
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingProbabilityarXiv
  3. On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels
    Emmanuel Gnabeyeu, Gilles Pagès
    HALPreprintCC BY 4.0Full textAnalysis & PDEsDynamical systemsHALarXiv
  4. Optimal Resource Extraction under Distribution Learning and Infinite-Horizon Stochastic Hamilton--Jacobi Equations
    Ulrich Horst, Jinniao Qiu, Yang Yang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  5. State-law dynamics of McKean-Vlasov stochastic reaction-diffusion equations on ℝn: pullback random attractors and zero-noise stability
    Guifen Liu, Yangrong Li
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{bergerhausen2026stability,
  title = {{Stability results for distribution-dependent stochastic Volterra equations}},
  author = {Martin Bergerhausen and David J. Prömel},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30736},
  eprint = {2608.30736},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30736},
}
RIS
TY  - UNPB
TI  - Stability results for distribution-dependent stochastic Volterra equations
AU  - Martin Bergerhausen
AU  - David J. Prömel
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30736
UR  - https://arxiv.org/abs/2608.30736
AB  - We investigate stability properties of distribution-dependent stochastic Volterra equations with respect to changes in the coefficients, the Volterra kernels, and the initial condition. Under Lipschitz continuity assumptions on the coefficients, we first derive quantitative stability estimates for strong solutions with explicit error bounds. We then prove a general convergence theorem for strong solutions under substantially weaker assumptions, replacing Lipschitz continuity by a continuity assumption together with uniform linear growth of the approximating sequence. Finally, we study the associated distribution-dependent Volterra local martingale problem and prove the stability of its solutions under convergence of the coefficients, kernels, and initial distributions.
ER  -