This 3rd edition provides an insight into the mathematical crossroads
formed by functional analysis (the macroscopic approach), partial
differential equations (the mesoscopic approach) and probability (the
microscopic approach) via the mathematics needed for the hard parts of
Markov processes. It brings these three fields of analysis together,
providing a comprehensive study of Markov processes from a broad
perspective. The material is carefully and effectively explained,
resulting in a surprisingly readable account of the subject.
The main focus is on a powerful method for future research in elliptic
boundary value problems and Markov processes via semigroups, the Boutet
de Monvel calculus. A broad spectrum of readers will easily appreciate
the stochastic intuition that this edition conveys. In fact, the book
will provide a solid foundation for both researchers and graduate
students in pure and applied mathematics interested in functional
analysis, partial differential equations, Markov processes and the
theory of pseudo-differential operators, a modern version of the
classical potential theory.