On the Existence of Feller Semigroups with Boundary Conditions
Author | : Kazuaki Taira |
Publisher | : American Mathematical Soc. |
Total Pages | : 81 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 0821825356 |
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This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups with Ventcel' (Wentzell) boundary conditions. This paper considers the non-transversal case and solves from the viewpoint of functional analysis the problem of construction of Feller semigroups for elliptic Waldenfels operators. Intuitively, our result may be stated as follows: One can construct a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it "dies" at which time it reaches the set where the absorption phenomenon occurs.