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2022 An application of the Gaussian correlation inequality to the small deviations for a Kolmogorov diffusion
Marco Carfagnini
Author Affiliations +
Electron. Commun. Probab. 27: 1-7 (2022). DOI: 10.1214/22-ECP459

Abstract

We consider an iterated Kolmogorov diffusion Xt of step n. The small ball problem for Xt is solved by means of the Gaussian correlation inequality. We also prove Chung’s laws of iterated logarithm for Xt both at time zero and infinity.

Funding Statement

Research was supported in part by NSF Grants DMS-1712427 and DMS-1954264.

Acknowledgments

The author thanks Davar Khoshnevisan and Zhan Shi for suggesting the Gaussian correlation inequality [18, 12].

Citation

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Marco Carfagnini. "An application of the Gaussian correlation inequality to the small deviations for a Kolmogorov diffusion." Electron. Commun. Probab. 27 1 - 7, 2022. https://doi.org/10.1214/22-ECP459

Information

Received: 2 January 2022; Accepted: 22 February 2022; Published: 2022
First available in Project Euclid: 8 March 2022

Digital Object Identifier: 10.1214/22-ECP459

Subjects:
Primary: 60F17
Secondary: 60F15 , 60G51 , 60J65

Keywords: Diffusion processes , Functional limit laws , Kolmogorov diffusion , small ball problem

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