Fractional Brownian motion stationary and self-similar increments. It has stationary increments: For "H" > ½ the process exhibits long-range dependence, Sample-paths are almost nowhere differentiable. However, almost-all trajectories are locally Hölder continuous of any order strictly less than "H": for each such trajectory, for every "T" > 0 and for every "ε" > 0 there exists a (random) constant "c" such that for 0 < "s","t" < "T". With probability 1, the graph of "B"("t") has both Hausdorff dimension and box dimension of 2−"H". As for regular Brownian motion, one can define stochastic integrals with respect to fractional Brownian motion, usually called "fractional
Schramm–Loewner evolution evolution is a probability measure on planar curves, given as the image of Wiener measure under this map. In general the curve γ need not be simple, and the domain "D" is not the complement of γ([0,"t"]) in "D", but is instead the unbounded component of the complement. There are two versions of SLE, using two families of curves, each depending on a non-negative real parameter κ: SLE depends on a choice of Brownian motion on the boundary of the domain, and there are several variations depending on what sort of Brownian motion is used: for example it might start