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2015 Necessary and sufficient conditions for the continuity of permanental processes associated with transient Lévy processes
Michael Marcus, Jay Rosen
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Electron. Commun. Probab. 20: 1-6 (2015). DOI: 10.1214/ECP.v20-4183

Abstract

Let $u^{\beta}(x,y)$ be the $\beta$-potential density of a transient Lévy process $\overline Y$ and $X_{\alpha}=\{X_{\alpha,x}, x\in R \}$ be the $\alpha$-permanental process determined by $u^{\beta}(x,y)$. Let $\overline L=\{\overline L_{t}^{x}, (t,x),\in R_{+}\times R \}$ be the local time process of $\overline Y$ and let $G=\{G_{x}, x\in R\}$ be the stationary mean zero Gaussian process with covariance $u^{\beta}(x,y)+ u^{\beta}(y,x)$. Then the processes $X_{\alpha}$, $\overline L$ and $G$ are either all continuous almost surely or all unbounded almost surely. Therefore, the well known necessary and sufficient condition for the continuity of $\overline L$ and $G$ is also a necessary and sufficient condition for the continuity of $X_{\alpha}$.

Citation

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Michael Marcus. Jay Rosen. "Necessary and sufficient conditions for the continuity of permanental processes associated with transient Lévy processes." Electron. Commun. Probab. 20 1 - 6, 2015. https://doi.org/10.1214/ECP.v20-4183

Information

Accepted: 4 August 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1325.60072
MathSciNet: MR3384115
Digital Object Identifier: 10.1214/ECP.v20-4183

Subjects:
Primary: 60G51
Secondary: 60G17, 60G99

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