Joint distribution of the process and its sojourn time for pseudo-processes governed by high-order heat equation

Abstract

Consider the high-order heat-type equation $\partial u/\partial t=\pm {\partial }^{N}u/\partial x^N$ for an integer $N>2$ and introduce the related Markov pseudo-process $(X(t){)}_{t\ge 0}$. In this paper, we study the sojourn time $T(t)$ in the interval $[0,+\infty )$ up to a fixed time $t$ for this pseudo-process. We provide explicit expressions for the joint distribution of the couple $(T(t),X(t))$.

References in corpus (1)

• First hitting time and place, monopoles and multipoles for pseudo-processes driven by the equation $\partial /\partial t=\pm {\partial }^N/\partial x^N$

Cited by in corpus (1)

• Sojourn Times for the One Dimensional Grover Walk