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Thesis

Ergodic and algebraic properties of transfer operators for products of random matrices

Abstract:

A recent paper by Pollicott in 2010 presented an efficient algorithm for computing the Lyapunov exponent of i.i.d. random products of positive matrices. The aim of this thesis is to generalise some of the aspects of Pollicott's approach to Markovian and more general matrix products using the theory of transfer operators. Some minor mistakes in Pollicott's original paper are corrected in the thesis. The possibility of further generalising the algorithm using the theory of operator algebras is discussed in the last chapter.

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Department:
Department of Statistics, University of Oxford
Role:
Supervisor
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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