Electronic Journal of Probability

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 and Valentina Cammarota

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

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 28, 895-931.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819813

Digital Object Identifier
doi:10.1214/EJP.v15-782

Mathematical Reviews number (MathSciNet)
MR2653948

Zentralblatt MATH identifier
1231.60032

Subjects
Primary: 60G20: Generalized stochastic processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J05: Discrete-time Markov processes on general state spaces

Keywords
pseudo-process joint distribution of the process and its sojourn time Spitzer's identity

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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. Electron. J. Probab. 15 (2010), paper no. 28, 895--931. doi:10.1214/EJP.v15-782. https://projecteuclid.org/euclid.ejp/1464819813


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