Subordinators and the actions of permutations with quasi-invariant measure

We introduce a class of probability measures in the space of virtual permutations associated with subordinators (i.e., processes with stationary positive independent increments). We prove that these measures are quasi-invariant under both left and right actions of the countable symmetric group $\mathfrak S_\infty$, and a simple formula for the corresponding cocycle is obtained. In case of a stable subordinator, we find the value of the spherical function of a constant vector on the class of transpositions. Bibliography: 19 titles.