Dual Skew Products, Genericity of the Exactness Property and Finance

Let us consider two homeomorphims S0, S1 of the interval I = [0, 1] onto itself. They determine the random walk on I as follows: x goes to S0(x) with probability p and x goes to S1(x) with probability q. Random walks on I may be realized as transformations of a larger space. Let Ω be the space {0, 1}N , N = {0, 1, 2, . . .}, with the (p, q)-measure μp on (Ω,B), where B is the Borel product σ-algebra and (p, q) is a prabability vector. Let σ be the onesided shift on Ω. In the space Ω × I we define the skew product