Abstract.
We consider diffusions corresponding to the generator
for continuous with γ i nonnegative. We show uniqueness for the corresponding martingale problem under certain non-degeneracy conditions on b i , γ i and present a counter-example when these conditions are not satisfied. As a special case, we establish uniqueness in law for some classes of super-Markov chains with state dependent branching rates and spatial motions.
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Received: 31 March 2001 / Revised version: 6 November 2001 / Published online: 1 July 2002
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Athreya, S., Barlow, M., Bass, R. et al. Degenerate stochastic differential equations and super-Markov chains. Probab Theory Relat Fields 123, 484–520 (2002). https://doi.org/10.1007/s004400100191
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DOI: https://doi.org/10.1007/s004400100191