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We study the first passage time processes of anomalous diffusion on selfsimilar curves in two dimensions. The scaling properties of the mean squaredisplacement and mean first passage time of the ballistic motion, fractionalBrownian motion and subordinated walk on different fractal curves (loop erasedrandom walk, harmonic explorer and percolation front) are derived. We alsodefine natural parametrized subordinated Schramm Loewner evolution (NS-SLE) asa mathematical tool that can model diffusion on fractal curves. The scalingproperties of the mean square displacement and mean first passage time forNS-SLE are obtained by numerical means.

First passage time processes and subordinated SLE