Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29202

Authors: Wang, Qingsong, Dorogovtsev, A. A.

Institutions: Jilin Police College, National Academy of Sciences of Ukraine, Institute of Mathematics

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W7223213152

Cites: 1

Cited by:

Related to: 10