On the Equality of Sharp and Germ - Fields for Gaussian Processes and Fields

2000 Mathematics Subject Classification: 60G15, 60G60; secondary 31B15, 31B25, 60H15We investigate the relationship between the sigma-field and the infinitesimal or germ sigma-field

An improved bound for the Gaussian concentration inequality

In this note, we provide an improved bound for the Gaussian concentration inequality. Our proof is short and bases on the integration-by-parts formula for the gaussian measure.Comment: 4 page

Necessary and Sufficient Conditions for H\"older Continuity of Gaussian Processes

The continuity of Gaussian processes is extensively studied topic and it culminates in the Talagrand's notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the H\"older continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov-\v{C}entsov condition