On a spectral theorem and its application to Lipschitzian kernels. (Sur un théorème spectral et son application aux noyaux lipschitziens.) (French) Zbl 0772.60049

Hennion, Hubert

Proc. Am. Math. Soc. 118, No. 2, 627-634 (1993).

Summary: The aim of this note is to point out that the Ionescu Tulcea and Marinescu theorem can be reinforced, using a Nussbaum formula for the essential spectral radius of an operator. In this stronger version, this theorem is suitable for the spectral analysis of Lipschitzian, positive, not necessarily Markovian kernels, Ruelle theorem follows. As an application to probability theory, a large deviation theorem is proved.

MSC:

60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
28D99	Measure-theoretic ergodic theory
60F10	Large deviations

Keywords:

essential spectral radius of an operator; Ruelle theorem; large deviation theorem