Abstract
In this final chapter we study a class of degenerate boundary value problems for second-order elliptic integro-differential operators, called Waldenfels operators, and generalize Theorems 1.2, 1.3, and 1.4 (Theorems 1.6, 1.8 and 1.9). As an application, we construct a Feller semigroup corresponding to such a physical phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it “dies” at the time when it reaches the set where the particle is definitely absorbed, generalizing Theorem 1.5 (Theorem 1.7). The results discussed here are adapted from Taira [Ta6] (cf. GarroniMenaldi [GM] and Galakhov-Skubachevskiĭ [GB]).
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© 2004 Springer-Verlag Berlin Heidelberg
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Taira, K. (2004). Boundary Value Problems for Waldenfels Operators. In: Semigroups, Boundary Value Problems and Markov Processes. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09857-8_14
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DOI: https://doi.org/10.1007/978-3-662-09857-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07371-7
Online ISBN: 978-3-662-09857-8
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