How one should "imagine" the paths of a Cauchy process?
Do they behave similarly like the Dirichlet function in a sense that they have countable many (though infinite many) jumps located dense on the time line and they are nowhere-continuous with probability 1, i.e. every time instant is a discontinuity point of the path with probability 1.
Or are they rather similar to the following example given in the attached question in a sense that the trajectories of a Cauchy process are continuous almost surely out of the set of the jump instants (which set has zero Lebesgue-measure since the number of jumps is countable), i.e. the path of a Cauchy process is almost surely continuous in every $t$ except in those countable many time instants $t$ when $X_{t}-X_{t-}>0$?
The mentioned question is below: Show that the function $f$ is continuous only at the irrational points
