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.