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Small deviations for integrators in terms of Itô--Wiener expansions

  • Qingsong Wang
  • A. A. Dorogovtsev
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Abstract

In this paper, we investigate small deviations for a class of Gaussian processes, known as integrators. In general, such processes are non-Markovian and may even fail to be semimartingales. First, we investigate small deviations for the multi-dimensional Wiener process, focusing on the asymptotic behavior of the Fourier--Wiener transform of the associated hitting event. We analyze the Fourier--Wiener transform and the separate summands in its Itô--Wiener expansion. Then, we establish the asymptotic limits of the associated multiple integrals with heat kernels. Finally, we obtain the small deviation asymptotic result for the integrator η associated with the continuous linear operator.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026small,
  title = {{Small deviations for integrators in terms of Itô--Wiener expansions}},
  author = {Qingsong Wang and A. A. Dorogovtsev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29202},
  eprint = {2610.29202},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29202},
}
RIS
TY  - UNPB
TI  - Small deviations for integrators in terms of Itô--Wiener expansions
AU  - Qingsong Wang
AU  - A. A. Dorogovtsev
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29202
UR  - https://arxiv.org/abs/2610.29202
AB  - In this paper, we investigate small deviations for a class of Gaussian processes, known as integrators. In general, such processes are non-Markovian and may even fail to be semimartingales. First, we investigate small deviations for the multi-dimensional Wiener process, focusing on the asymptotic behavior of the Fourier--Wiener transform of the associated hitting event. We analyze the Fourier--Wiener transform and the separate summands in its Itô--Wiener expansion. Then, we establish the asymptotic limits of the associated multiple integrals with heat kernels. Finally, we obtain the small deviation asymptotic result for the integrator η associated with the continuous linear operator.
ER  -