Self-exciting piecewise linear processes (2017)
The paper concerns a piecewise linear process controlled by the set of velocities cnn≥0 consecutively switched after exponentially distributed, Exp(λn), n ≥ 0, time intervals. The distribution of such process is studied in detail, including the distribution of the first passage time through the constant boundary. The processes which moves by alternating patterns and with a double jump component are also studied