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The martingale problem with sticky reflection conditions, and a system of particles interacting at the boundary. (English) Zbl 0643.60042
Solving certain martingale problems the author constructs a class of continuous processes satisfying Wentzell’s boundary conditions in the case of possibly completely degenerated generators. Time change and weak compactness arguments are used. As an example, a system of particles with an interaction in the sojourn term is constructed by a limiting procedure.
Reviewer: R.Mikulevičius

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60B10 Convergence of probability measures
60G44 Martingales with continuous parameter
60J50 Boundary theory for Markov processes
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