A Hanson-Russo-type law of the iterated logarithm for fractional Brownian motion
Let \(\{B_ H(t),\;t\geq 0\}\) be a fractional Brownian motion of index \(H\) and consider its increments \(X_ n(u)=\beta_ n(B_ H(n+ug(n))-B_ H(n))\) \((0\leq u\leq 1)\) with a given increment function \(g(n)\) and a suitable normalizing factor \(\beta_ n\). The author proves that the set of the limit points of \(X_ n(\cdot)\) \((n\to\infty)\) is a natural generalization of the Strassen class.
scientific article; zbMATH DE number 178026
scientific article