Lachal, Aimé; Cammarota, Valentina Joint distribution of the process and its sojourn time on the positive half-line for pseudo-processes governed by high-order heat equation. (English) Zbl 1231.60032 Electron. J. Probab. 15, Paper No. 28, 895-931 (2010). Summary: 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 \((X(t))_{t\geq 0}\). 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 \((T(t),X(t))\). Cited in 7 Documents MSC: 60G20 Generalized stochastic processes 60J25 Continuous-time Markov processes on general state spaces 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J05 Discrete-time Markov processes on general state spaces Keywords:pseudo-process; joint distribution of the process and its sojourn time; Spitzer’s identity PDFBibTeX XMLCite \textit{A. Lachal} and \textit{V. Cammarota}, Electron. J. Probab. 15, Paper No. 28, 895--931 (2010; Zbl 1231.60032) Full Text: DOI arXiv EMIS