Ergodic Control in L 1

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Ergodic problems in differential games

We present and study a notion of ergodicity for deterministic zerosum differential games that extends the one in classical ergodic control theory to systems with two conflicting controllers. We show its connections with the existence of a constant and uniform long-time limit of the value function of finite horizon games, and characterize this property in terms of Hamilton-Jacobi-Isaacs equation...

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Singular Ergodic Control for Multidimensional Gaussian-Poisson Processes

Singular control for multidimensional Gaussian-Poisson processes with a long-run (or ergodic) and a discounted criteria are discussed. The dynamic programming yields the corresponding Hamilton-JacobiBellman equations, which are discussed. Full details on the proofs and further extensions are left for coming works.

Coexistence of Uniquely Ergodic Subsystems of Interval Mapping

Ye, X.D., Coexistence of uniquely ergodic subsystems of interval mappings, Theoretical Computer Science 123 (1994) 1677181. We prove that if (1.f) has a uniquely ergodic subsystem (X,f] x, x), then fo$ every sqh, (I,f) has a uniquely ergodic subsystem (Y,f],, p) such thatfs=s, where l=[O, l].f~C(l,l).