Packing-dimension profiles and fractional Brownian motion

Packing-dimension Profiles and Fractional Brownian Motion

In order to compute the packing dimension of orthogonal projections Falconer and Howroyd (1997) introduced a family of packing dimension profiles Dims that are parametrized by real numbers s > 0. Subsequently, Howroyd (2001) introduced alternate s-dimensional packing dimension profiles P-dims and proved, among many other things, that P-dimsE = DimsE for all integers s > 0 and all analytic sets ...

Packing Measure of the Sample Paths of Fractional Brownian Motion

Let X(t) (t ∈ R) be a fractional Brownian motion of index α in Rd. If 1 < αd , then there exists a positive finite constant K such that with probability 1, φ-p(X([0, t])) = Kt for any t > 0 , where φ(s) = s 1 α /(log log 1 s ) 1 2α and φ-p(X([0, t])) is the φ-packing measure of X([0, t]).

Dimension of Fractional Brownian motion with variable drift

Let X be a fractional Brownian motion in R. For any Borel function f : [0, 1] → R, we express the Hausdorff dimension of the image and the graph of X+f in terms of f . This is new even for the case of Brownian motion and continuous f , where it was known that this dimension is almost surely constant. The expression involves an adaptation of the parabolic dimension previously used by Taylor and ...

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Tempered fractional Brownian motion