Feller Semigroups and Boundary Value Problems

Kazuaki Taira ()
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Kazuaki Taira: University of Tsukuba, The College of Mathematics

Chapter Chapter 24 in Real Analysis Methods for Markov Processes, 2024, pp 623-643 from Springer

Abstract: Abstract TheBoundary value problem purposeFeller semigroup of this chapter is to prove a general existence theorem for Feller semigroups in terms of boundary value problems (Theorem 24.9), following the main idea of Taira [148, Sect. 9.6] (cf. Bony–Courrège–Priouret [15] and Sato–Ueno [124]). Intuitively, Theorem 24.9 asserts that we can “piece together” a Markov process on the boundary $$\partial \Omega $$ ∂ Ω with A-diffusion in the interior $$\Omega $$ Ω to construct a Markov process on the closure $$\overline{\Omega } = \Omega \cup {\partial \Omega }$$ Ω ¯ = Ω ∪ ∂ Ω (see Remark 24.5).

Date: 2024
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DOI: 10.1007/978-981-97-3659-1_24

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