1971/01/01 by Sidney C. Port, Charles J. Stone · 2 citations
Physics and Astronomy · Mathematics · #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and statistical mechanics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.5802/aif.398
openalex publication_date 1971/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
This second part of our two part work on i.d. process has four main goals: (1) To develop a potential operator for recurrent i.d. (infinitely divisible) processes and to use this operator to find the asymptotic behavior of the hitting distribution and Green’s function for relatively compact sets in the recurrent case. (2) To develop the appropriate notion of an equilibrium measure and Robin’s constant for Borel sets. (3) To establish the asymptotic behavior questions of a potential theoretic nature for both transient and recurrent processes. These include finding all solutions of Poisson type equations that are bounded from below, where the role of the Laplace operator is played by either the infinitesimal generator of the process or of the process stopped on a closed set, and of finding all solutions that are bounded from below for Dirichlet type problems on closed sets.