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2010 Joint Distribution of the Process and its Sojourn Time on the Positive Half-Line for Pseudo-Processes Governed by High-Order Heat Equation
Aimé Lachal, Valentina Cammarota
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Electron. J. Probab. 15: 895-931 (2010). DOI: 10.1214/EJP.v15-782

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

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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

Information

Accepted: 17 June 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1231.60032
MathSciNet: MR2653948
Digital Object Identifier: 10.1214/EJP.v15-782

Subjects:
Primary: 60G20
Secondary: 60J05, 60J25, 60K35

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