  The probabilistic symbol is defined as the right-hand side derivative at time
zero of the characteristic functions corresponding to the one-dimensional
marginals of a time-homogeneous stochastic process. As described in various
contributions to this topic, the symbol contains crucial information concerning
the process. When leaving time-homogeneity behind, a modification of the symbol
by inserting a time component is needed. In the present article we show the
existence of such a time-dependent symbol for non-homogeneous It\^o processes.
Moreover, for this class of processes we derive maximal inequalities which we
apply to generalize the Blumenthal-Getoor indices to the non-homogeneous case.
These are utilized to derive several properties regarding the paths of the
process, including the asymptotic behavior of the sample patsh, the existence
of exponential moments and the finiteness of p-variation. In contrast to many
situations where non-homogeneous Markov processes are involved, the space-time
process cannot be utilized when considering maximal inequalities.
