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Projections of scaled bessel processes

Kardaras, Constantinos ORCID: 0000-0001-6903-4506 and Ruf, Johannes (2019) Projections of scaled bessel processes. Electronic Communications in Probability, 24. ISSN 1083-589X

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Identification Number: 10.1214/19-ECP246

Abstract

Let X and Y denote two independent squared Bessel processes of dimension m and n-m, respectively, with n ≥ 2 and m ∈ [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.

Item Type: Article
Official URL: https://www.imstat.org/journals-and-publications/e...
Additional Information: © 2019 The Authors
Divisions: Statistics
Mathematics
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Date Deposited: 04 Jun 2019 11:24
Last Modified: 20 Sep 2021 03:11
URI: http://eprints.lse.ac.uk/id/eprint/100939

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