Semigroups, Boundary Value Problems and Markov Processes

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.