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2019 Projections of scaled Bessel processs
Constantinos Kardaras, Johannes Ruf
Electron. Commun. Probab. 24: 1-11 (2019). DOI: 10.1214/19-ECP246

Abstract

Let $X$ and $Y$ denote two independent squared Bessel processes of dimension $m$ and $n-m$, respectively, with $n\geq 2$ and $m \in [0, n)$, making $X+Y$ a squared Bessel process of dimension $n$. For appropriately chosen function $s$, the process $s (X+Y)$ is a local martingale. We study the representation and the dynamics of $s(X+Y)$, projected on the filtration generated by $X$. This projection is a strict supermartingale if, and only if, $m<2$. The finite-variation term in its Doob-Meyer decomposition only charges the support of the Markov local time of $X$ at zero.

Citation

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Constantinos Kardaras. Johannes Ruf. "Projections of scaled Bessel processs." Electron. Commun. Probab. 24 1 - 11, 2019. https://doi.org/10.1214/19-ECP246

Information

Received: 3 January 2019; Accepted: 2 June 2019; Published: 2019
First available in Project Euclid: 3 July 2019

zbMATH: 07088984
MathSciNet: MR3978692
Digital Object Identifier: 10.1214/19-ECP246

Subjects:
Primary: 60G44, 60G48, 60H10, 60J55, 60J60

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