Joint distribution of the process and its sojourn time on the positive half-line for pseudo-processes governed by high-order heat equation.

Consider the high-order heat-type equation ∂u/∂t = ±∂Nu/∂xN for an integer N > 2 and introduce the related Markov pseudo-process (X(t))t≥0. In this paper, we study the sojourn time T(t) in the interval [0, +∞) up to a fixed time t for this pseudo-process. We provide explicit expressions for the joint distribution of the couple (T(t),X(t))