In part I, we have obtained a measure preserving group action which is isomorphic to SL(2, R) Nrom this action we have deduced a symmetric roerty called P. Lvy's roeetie ivriee o Broie motion. In this art we, using the terms of theory of unitary representation, determine the class f the above action a dierete erie rereetatio o index 2. 4. Stochastic integral of Wiener tTpe. Let {X(t; ); t eR} be a Gaussian roeess with continuous ath and e (R) be a test function. Define an integral of Wiener type; ( 6 )