In this thesis the CRISPR-Cas9 mechanism, a promising mechanism for geneediting, is considered. Closed form expressions are derived for the probability and time to cleave or unbind for the associated Cas9 protein. The mechanism can be modelled mathematically by a birth and death process, therefore the expressions could be derived using Markov chains and semigroups. The expressions are compared to simulations and interpreted using the model of hybridization kinetics. Finally the moment generating function of the stopping time is derived for two special Markov processes, i.e. a random walk and a Brownian motion with drift. This was done using martingales.