May 2014
Intermediate to advanced
258 pages
6h 11m
English
Content preview from Markov Chains: Analytic and Monte Carlo Computations
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1.3 Natural duality: algebraic approach
An algebraic study based on the natural duality between the space of signed measures 
and the space of bounded functions 
will provide some structural results. These results are quite complete for finite state spaces 
. The complete study for arbitrary discrete 
will be done later using probabilistic techniques. A reader for which this is the main interest may go directly to Section 1.4.
1.3.1 Complex eigenvalues and spectrum
1.3.1.1 Some reminders
The eigenvalues of the operator
are given by all 
such that 
is not injective as an operator on 
.
The eigenspace of is the kernel
and its nonzero elements are called eigenvectors. Hence, in is an eigenvector ...
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