Limit theorems for nonhomogeneous semi-Markov processes

Limit Theorems for Multidimensional Markov Processes

An informal exposition of some recent results and conjectures. A multidimensional Markov process (mdmp) is a dynamical system (K, m, T) where: K space of the sequences of symbols from a finite alphabet / = (α, fo,... z) indexed by the elements η e Z = lattice formed by the d-ples of integers. K is regarded as K = TίηeZd I i.e. as a product space of copies of/; furthermore / is topologized by th...

Strong Law of Large Numbers and Central Limit Theorems for functionals of inhomogeneous Semi-Markov processes

Abstract: Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of R. Pyke and R. Schaufele (1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example in finance and insurance. Unfortunately, no limit theorems have been ...

Spectral Theory and Limit Theorems for Geometrically Ergodic Markov Processes

Consider the partial sums {St} of a real-valued functional F (Φ(t)) of a Markov chain {Φ(t)} with values in a general state space. Assuming only that the Markov chain is geometrically ergodic and that the functional F is bounded, the following conclusions are obtained: Spectral theory: Well-behaved solutions f̌ can be constructed for the “multiplicative Poisson equation” (eP )f̌ = λf̌ , where P is...

Limit theorems for stationary Markov processes with L2-spectral gap

Let (Xt, Yt)t∈T be a discrete or continuous-time Markov process with state space X × R where X is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. (Xt, Yt)t∈T is assumed to be a Markov additive process. In particular, this implies that the first component (Xt)t∈T is also a Markov process. Markov random walks or additive f...

The KTH Visit in Semi-Markov Processes