Skip to content
DraconiticResearch
Search Sources API
190,860 studies31 sourcesUpdated 53 min ago
PreprintarXiv licencearXiv

Small-time annealed large deviations principle for one-dimensional diffusions in a random environment

  • Yiduo Wang
  • Saisai Yang
  • Tusheng Zhang
Open at sourcePDFDOICite

Abstract

In this paper, we establish a small-time annealed path large deviation principle for one-dimensional diffusions in a random environment associated with the generator ℒW f(x)=e−ρ(x,W)(ea(x,W)f'(x))'. The coefficients {ρ(x,·):x∈ℝ} and {a(x,·):x∈ℝ} are random. We assume that for each fixed realization of the environment, ρ and a are continuous and locally exponentially integrable, and that the support of the associated intrinsic coordinates is compact and non-collapsing. This framework includes the extensively studied Brox diffusion dXt=dBt−1/2Ẇ(Xt) dt, where B is a standard Brownian motion and W is an independent two-sided Brownian motion representing the environment. The Itô--McKean representation of the diffusions and the estimates of the first exit probabilities derived via Moser iteration play a crucial role.

Related

  1. Small-time asymptotics of heat kernels of one-dimensional diffusions in a random environment
    Yiduo Wang, Saisai Yang, Tusheng Zhang
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  2. Annealed Survival Probability of Random Walk in an Inhomogeneous Poisson Environment of Mobile Traps
    Pradeeptha R Jain
    arXivPreprintCC BY 4.0Full textMathematical physicsProbabilityarXiv
  3. Selection principle for Weak KAM solutions on ℝn via large deviation principle for diffusions
    Yuan Gao, Yuxi Han
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv
  4. Almost global large deviations principle for the KdV equation
    Riccardo Berforini d'Aquino, Ricardo Grande
    HALPreprintCC BYFull textMathematical physicsHAL
  5. Limit theorems for one-dimensional diffusions: reflected, skew, sticky, skew-sticky, and snapping-out limits
    Andrey Pilipenko, Gilles Vilmart
    arXivPreprintCC BY-NC-ND 4.0Full textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{wang2026smalltime,
  title = {{Small-time annealed large deviations principle for one-dimensional diffusions in a random environment}},
  author = {Yiduo Wang and Saisai Yang and Tusheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.26834},
  eprint = {2608.26834},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.26834},
}
RIS
TY  - UNPB
TI  - Small-time annealed large deviations principle for one-dimensional diffusions in a random environment
AU  - Yiduo Wang
AU  - Saisai Yang
AU  - Tusheng Zhang
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2608.26834
UR  - https://arxiv.org/abs/2608.26834
AB  - In this paper, we establish a small-time annealed path large deviation principle for one-dimensional diffusions in a random environment associated with the generator ℒ_W f(x)=e^−ρ(x,W)(e^a(x,W)f'(x))'. The coefficients {ρ(x,·):x∈ℝ} and {a(x,·):x∈ℝ} are random. We assume that for each fixed realization of the environment, ρ and a are continuous and locally exponentially integrable, and that the support of the associated intrinsic coordinates is compact and non-collapsing. This framework includes the extensively studied Brox diffusion dX_t=dB_t−1/2Ẇ(X_t) dt, where B is a standard Brownian motion and W is an independent two-sided Brownian motion representing the environment. The Itô--McKean representation of the diffusions and the estimates of the first exit probabilities derived via Moser iteration play a crucial role.
ER  -