Multiplicative Operator Functionals of a Markov Process

Almost multiplicative linear functionals and approximate spectrum

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

C*-algebras on r-discrete Abelian Groupoids

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

Girsanov and Feynman-kac Type Transformations for Symmetric Markov Processes

– Studied in this paper is the transformation of an arbitrary symmetric Markov process X by multiplicative functionals which are the exponential of continuous additive functionals of X having zero quadratic variations. We characterize the transformed semigroups by their associated quadratic forms. This is done by first identifying the symmetric Markov process under Girsanov transform, which may...

Multiplicative bijective maps on standard operator algebras

Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov Processes

In this paper we continue the investigation of the spectral theory and exponential asymptotics of primarily discrete-time Markov processes, following Kontoyiannis and Meyn [34]. We introduce a new family of nonlinear Lyapunov drift criteria, which characterize distinct subclasses of geometrically ergodic Markov processes in terms of simple inequalities for the nonlinear generator. We concentrat...