We consider an iterated Kolmogorov diffusion of step n. The small ball problem for is solved by means of the Gaussian correlation inequality. We also prove Chung’s laws of iterated logarithm for both at time zero and infinity.
Research was supported in part by NSF Grants DMS-1712427 and DMS-1954264.
The author thanks Davar Khoshnevisan and Zhan Shi for suggesting the Gaussian correlation inequality [18, 12].
"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