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

Valentina Cammarota; Aimé Lachal

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arXiv · 1001.4201

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

Valentina Cammarota·Aimé Lachal

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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 $(T(t),X(t))$.

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Valentina Cammarota, Aimé Lachal. 2010-01-23. Joint distribution of the process and its sojourn time for pseudo-processes governed by high-order heat equation. https://arxiv.org/abs/1001.4201

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