Title: Semigroups, Boundary Value Problems and Markov Processes
Description: The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. More precisely this book is devoted to the functional-analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators which includes as particular cases the Dirichlet and Robin problems. This class of boundary value problems provides a new example of analytic semigroups. As an application, we construct a strong Markov process corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the set where the particle is definitely absorbed.
Subjects: Harmonic analysis, Mathematics, Differential equations, partial, Functional analysis, Distribution (Probability theory), Markov processes, Semigroups, Boundary value problems, Partial Differential equations, Abstract Harmonic Analysis, Probability Theory and Stochastic Processes