Abstract
A typical class of generalized OU-processes arise as small-branching fluctuation limits of subcritical immigration superprocesses around their equilibrium means. In this chapter, we first establish such a fluctuation limit theorem in the space of Schwartz distributions. A stronger result is then proved which shows that the convergence actually holds in a suitable weighted Sobolev space. To avoid complicated regularity assumptions, we only consider the case where the spatial motion is a Brownian motion with killing.
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© 2011 Springer-Verlag Berlin Heidelberg
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Li, Z. (2011). Small-Branching Fluctuation Limits. In: Measure-Valued Branching Markov Processes. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15004-3_12
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DOI: https://doi.org/10.1007/978-3-642-15004-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15003-6
Online ISBN: 978-3-642-15004-3
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