TY - GEN
A1 - Nielsen, Adam
T1 - The Monte Carlo Computation Error of Transition Probabilities
N2 - In many applications one is interested to compute transition probabilities of a Markov chain.
This can be achieved by using Monte Carlo methods with local or global sampling points.
In this article, we analyze the error by the difference in the $L^2$ norm between the true transition probabilities and the approximation
achieved through a Monte Carlo method.
We give a formula for the error for Markov chains with locally computed sampling points. Further, in the case of reversible Markov chains, we will deduce a formula for the error when sampling points are computed globally.
We will see that in both cases the error itself can be approximated with Monte Carlo methods.
As a consequence of the result, we will derive surprising properties of reversible Markov chains.
T3 - ZIB-Report - 16-37
KW - Reversible Markov chain
KW - Monte Carlo methods
KW - Computation error
KW - Measurable state space
KW - Markov operator
Y1 - 2016
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/5993
UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-59933
SN - 1438-0064
ER -