Abstract
Consider the high-order heat-type equation $\partial_t u=\pm \partial^n_x u$ for an integer $n>2$ and introduce the related Markov pseudo-process $(X(t))_{t\geq0}$. 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 $(T(t),X(t))$.
Citation
Aimé Lachal. Valentina Cammarota. "Joint Distribution of the Process and its Sojourn Time on the Positive Half-Line for Pseudo-Processes Governed by High-Order Heat Equation." Electron. J. Probab. 15 895 - 931, 2010. https://doi.org/10.1214/EJP.v15-782
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