Local and uniform moduli of continuity of chi-square processes (Q2152567)

The authors show that when the Gaussian process \(\eta\) has a local or uniform modulus of continuity the related \(k/2\) chi-square process has a closely related local or uniform modulus of continuity. The main results are given in Theorem 1.1 (which seems to extend a similar result given by the authors [Asymptotic properties of permanental sequences. Related to birth and death processes and autoregressive Gaussian sequences. Cham: Springer (2021; Zbl 1486.60001)]) and in Theorem 1.2 (this result extend a good result given by the same authors in [Markov processes, Gaussian processes, and local times. Cambridge: Cambridge University Press (2006; Zbl 1129.60002)]).