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Focusing on advanced real analysis methods, this book explores the construction of Markov processes influenced by boundary conditions in probability theory. It examines the behavior of a Markovian particle governed by the Waldenfels operator and adhering to the Ventcel boundary condition, which encompasses various phenomena like diffusion, absorption, and jumps. The study delves into first-order Ventcel boundary value problems for second-order elliptic operators, employing Calderón-Zygmund theory to establish existence and uniqueness theorems in Sobolev and Besov spaces.
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Real Analysis Methods for Markov Processes, Kazuaki Taira
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- 2024
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