# Ms Kate Menzel**Honours graduate**
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Office: 721 |

## Honours thesis

**Accumulated reward in Markov reward models**

In this project we consider a number of methods which can be used to numerically
evaluate the moments of accumulated reward of a Markov reward model. Two
existing methods given by Castella et al. [3] are first summarised, then an alternative
approach is introduced, utilising path integral techniques. We find that the path
integral approach may be solved in two ways, using either an ordinary differential
equation solver or by way of matrix exponentials. These methods are initially given
in context of an irreducible process, but later are extended to the case of a reducible
process, where we find that certain methods, in particular the extremely efficient
matrix exponential method, do not necessarily work in all cases we consider. The
accumulated reward of a process is then given in a physical context where it is
considered as a possible measure of risk of extinction for a population. We find
that the measure does in fact summarise the risk of population extinction quite
effectively.