A one dimensional diffusion process X={X_t, 0 <= t <= T}, with drift b(x) and diffusion coefficient s(theta, x)=sqrt(theta) s(x) known up to theta>0, is supposed to switch volatility regime at some point t* in (0,T). On the basis of discrete time observations from X, the problem is the one of estimating the instant of change in the volatility structure t* as well as the two values of theta, say...</=>

The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity +v or -v. The changes of direction are governed by an...