Abstract:

Let $X=(X\-t)\-t≥0$ be a realvalued stochastic process which is selfsimilar with parameter $H>0$ and has stationary increments. Several results about themarginal distribution of $X\-1$ are given for $H≠1, $there is a bound, depending only on $H$, on the concentration function of
log$X\++\-1$. For all $H>0,X\-1$ cannot have any atomsexcept in certain trivial cases. Some lower bounds are given for the tails of the distribution of $X\-1$ in case $H>1.$ Finally, some results are given concerning the connectedness of  the support of  $X\-1.$

Key words: Stationary increment, Selfsimilar prcesses, Concentration function.