Abstract
The Brownian snake construction of quadratic superprocesses relies on the fact that the genealogical structure of the Feller diffusion can be coded by reflected Brownian motion. Our goal in this chapter is to explain a similar coding for the genealogy of continuous-state branching processes with a general branching mechanism ψ. The role of reflected Brownian motion will be played by a certain functional of a Lévy process with no negative jumps and Laplace exponent ψ. We first explain the key underlying ideas in a discrete setting.
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© 1999 Springer Basel AG
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Le Gall, JF. (1999). Lévy Processes and the Genealogy of General Continuous-state Branching Processes. In: Spatial Branching Processes, Random Snakes and Partial Differential Equations. Lectures in Mathematics ETH Zürich. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8683-3_8
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DOI: https://doi.org/10.1007/978-3-0348-8683-3_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-6126-6
Online ISBN: 978-3-0348-8683-3
eBook Packages: Springer Book Archive