Electronic Communications in Probability

Projections of scaled Bessel processs

Constantinos Kardaras and Johannes Ruf

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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.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 43, 11 pp.

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

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Primary: 60G44: Martingales with continuous parameter 60G48: Generalizations of martingales 60H10: Stochastic ordinary differential equations [See also 34F05] 60J55: Local time and additive functionals 60J60: Diffusion processes [See also 58J65]

Bessel process filtering local martingale local time

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Kardaras, Constantinos; Ruf, Johannes. Projections of scaled Bessel processs. Electron. Commun. Probab. 24 (2019), paper no. 43, 11 pp. doi:10.1214/19-ECP246. https://projecteuclid.org/euclid.ecp/1562119371

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