The distribution of the local time for "pseudoprocesses" and its connection with fractional diffusion equations

We prove that the pseudoprocesses governed by heat-type equations of order n[greater-or-equal, slanted]2 have a local time in zero (denoted by ) whose distribution coincides with the folded fundamental solution of a fractional diffusion equation of order 2(n-1)/n, n[greater-or-equal, slanted]2. The distribution of is also expressed in terms of stable laws of order n/(n-1) and their form is analyzed. Furthermore, it is proved that the distribution of is connected with a wave equation as n-->[infinity]. The distribution of the local time in zero for the pseudoprocess related to the Myiamoto's equation is also derived and examined together with the corresponding telegraph-type fractional equation.