The reflected Dirichlet space

Dirichlet Functions of Reflected Brownian Motion

We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes.

The classical Dirichlet space

D |f ′|2 dx dy. In particular, we will cover the basic structure of these functions their boundary values and their zeros along with two important operators that act on this space of functions the forward and backward shifts. This survey is by no means complete. For example, we will not cover the Toeplitz or Hankel operators on these functions, nor will we cover the important topic of interpola...

The Dirichlet space: a survey

6 The multiplier space and other spaces intrinsic to D theory 24 6.1 Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.2 The weakly factored space D D and its dual . . . . . . . . . . . 25 6.3 The Corona Theorem . . . . . . . . . . . . . . . . . . . . . . . . 27 6.3.1 The ∂-equation in the Dirichlet Space . . . . . . . . . . . 28 6.3.2 Corona Theorems and Complete Nev...

A Dirichlet Process Characterization of a Class of Reflected Diffusions

For a general class of stochastic differential equations with reflection that admit a Markov weak solution and satisfy a certain L continuity condition, p > 1, it is shown that the associated reflected diffusion can be decomposed as the sum of a local martingale and a continuous, adapted process of zero p-variation. In particular, when p = 2, this implies that the associated reflected diffusion...

The Dirichlet Space on the bi-disc