Oscillating processes with independent increments and nondegenerate Wiener component (Q808536)

The author relates his results on limit distribution for oscillating random walks [Probability theory and mathematical statistics, Proc. 5th Vilnius Conf., Vilnius/Lith. 1989, Vol. III, 170-171 (1990)]. Here, the oscillating process \(\zeta_ z(t)\) is defined by two homogeneous processes \(\xi_ 1(t)\) and \(\xi_ 2(t)\) with independent increments and nondegenerate Wiener components. Under a few restrictions, he establishes a relation of the form \[ \phi (\lambda,\alpha)=\lambda \int^{\infty}_{0}\exp (-\lambda t)E \exp \{i\alpha \zeta_ z(t)\}dt \] and finds the characteristic function of the ergodic distribution of the process.