Semigroups, Boundary Value Problems and Markov Processes

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Focusing on the intersection of Markov processes and elliptic boundary value problems, this book explores analytic semigroups related to degenerate boundary value problems for second-order elliptic integro-differential operators, specifically Waldenfels operators. It presents a functional analytic approach, proving new examples of analytic semigroups in various topologies. Additionally, the text constructs a strong Markov process representing a particle's movement through jumps and continuous paths until absorption. The methodology incorporates advanced techniques from partial differential equations and pseudo-differential operators.