Cores for Feller semigroups with an invariant measure

Feller Processes and Semigroups

For convenience, we can have a look at the list of materials contained in this lecture first. Note here we always consider the time-homogenous Markov processes. • Transition kernels μt, t ≥ 0 ←→ transition operators semigroup Tt, t ≥ 0. • Feller semigroup Tt, t ≥ 0 • Feller processes • existence • every Feller process has a cadlag version • regularization theorem for submartingale • strong Mark...

An Invariant Measure for Finitely Generated Rational Semigroups

For a nitely generated rational semigroup G we establish the existence of a probability measure = G on the Julia set J(G) which has a certain invariance property with respect to the semigroup.

Cores for generators of some Markov semigroups ∗

We consider a stochastic differential equation on Rd with Lipschitz coefficients. We find a core for the infinitesimal generator of the corresponding Markov process. Some applications, in particular, to well-posedness of Fokker–Planck equations are given. 2000 Mathematics Subject Classification AMS: 60H10, 60J35, 47D07.

On asymptotic properties of matrix semigroups with an invariant cone

Article history: Received 21 October 2011 Accepted 1 April 2012 Available online 18 May 2012 Submitted by H. Schneider AMS classification: 15B48 65H17 26A15 93C30

Invariant measure for an infinite neural network