Quadratic variation and energy

Abstract

It is well known that the concept of energy has played a fruitful role in potential theory and Markov processes. Cartan’s work [6] led to kernel-free potential theories of Beurling-Deny [2]. Since then many authors have worked on this, M. Fukushima [8], M. Silverstein [16], J. Bliedner [3], Berg-Forst [1], to name some. In these works, however, the main thrust is Hubert space theoretic.