Small ball estimates for Brownian motion and the Brownian sheet
Introduce the Hölder norm \(\| f\|_ \alpha=\sup(| f(t)- f(s)|/| t-s|^ \alpha)\). The authors study the asymptotic behaviour of \(P[\| W\|_ \alpha\leq\varepsilon]\) as \(\varepsilon\to 0\), where \(W\) is the Brownian motion. The corresponding results for the Brownian sheet are also considered.
scientific article; zbMATH DE number 423615