Abstract
Our objective is to study measure-valued diffusions which locally behave like DW-superprocesses, much in the same way as solutions to Ito–s stochastic differential equations behave locally like Brownian motions. This means that we want to consider processes in which the branching rate, γ, the spatial generator, A, and the drift, g, all depend on the current state of the system, Xt, or more generally on the past behaviour of the system, X|[0,t]. One suspects that these dependencies are listed roughly in decreasing order of difficulty. In this Chapter we present a general result of Dawson which, for a large class of interactive drifts, will give an explicit formula for the Radon-Nikodym derivative of law of the interactive model with respect to that of a driftless DW-superprocess.
Keywords
- Martingale Measure
- Local Martingale
- Martingale Problem
- Continuous Local Martingale
- Branch Particle System
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© 2002 Springer-Verlag Berlin Heidelberg
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(2002). Interactive Drifts. In: Bernard, P. (eds) Lectures on Probability Theory and Statistics. Lecture Notes in Mathematics, vol 1781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47944-9_8
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DOI: https://doi.org/10.1007/3-540-47944-9_8
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43736-9
Online ISBN: 978-3-540-47944-4
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