The verification of the delivered dose during or shortly after particle therapy (PT) with positron emission tomography (PET) is an (practical) approach for in vivo dosimetry. PET imaging is based on the detection of positron-electron annihilation photons. Irradiated tissue during PT leads to nuclear reactions and the production of +emitting radionuclides, creating a 3D activity distribution map. For therapy monitoring, the measured and a predicted activity distribution are compared. Monte Carlo (MC) simulations can accurately describe particle transport and interactions with matter in complex geometries, which makes them an important tool for calculated + activity distributions. In research and clinical studies it is used to develop novel techniques for range verifications in vivo. The open-source simulation platform GATE (Geant4 Application for Tomographic Emission), which encloses the MC based framework Geant4 as well as the computational power, made it feasible to perform complex simulations with patient data. The accuracy of the simulations strongly depends on the parameter definitions, e.g. physics models definitions, interaction and output properties. In this thesis the influence of simulation parameters e.g. step size, Houndsfield unit (HU) scale, data storage actor and primary particle numbers on the dose and +activity distributions is presented. The evaluation of the suitable physics model was performed by testing 16 different physic lists. In a simulation a 100 x 100 x 400 mm3. Polymethylmethacrylat (PMMA) phantom was irradiated with a proton beam of 106 particles at 110, 140 and 175 MeV, and the data were stored using the ProductionAndStopping actor. The results obtained from the simulations with different physics lists were compared with the experimental results from literature. The most compliant physics list was QGSP_BIC_HP, for all positron emitters and at all energies. The performed statistical analysis with 0.1 mm and 0.01 mm step size distances revealed a reduction of the uncertainty with increasing primary particle numbers for both step sizes. A reduction from 7% with 105 primary particles to 2% with 106 primary particles per beam, was observed for the 0.1 mm step size simulations. For the 0.01 mm step size setups, similar but slightly higher results were achieved. Simulations performed with 108 primary particles lead to the expected conclusion that the fluctuations of produced positron emitters would decrease compared to lower proton quantities. Resulting from the tendency of reducing statistical uncertainty with increasing primary particle numbers, the variances would be below 2%. Due to longer simulation times and the higher variances for produced positron emitter distributions, the decision felt for 0.1 mm step size. In terms of maximum number of primary particles for complex TP simulations, the highest performed quantity was used, namely 108. Homogenous phantoms (90 x 90 x 300 mm3.) were irradiated with a proton beam containing 107 particles at 140 MeV. Two different phantom setups were used to evaluate the range uncertainties influenced by the storage actors, namely ProductionAndStopping and CrossSectionProduction actor. Furthermore, the phantoms consisted of different insert materials with varying thickness, to investigate the behaviour of those actors and the range uncertainties of the produced C-11 and O-15 particles. Due to the low number of produced 10C particles, the positron emitter was not evaluated. The comparison of the behaviour of the storage actors, resulted in a favouring of the CrossSectionProduction actor over the ProductionAndStopping actor. The range uncertainty of the R50 distance of produced positron emitters could be visually evaluated for any insert thicknesses. For the ProductionAndStopping actor the visual range differences for the R50 distance of produced positron emitters were approximately 1 mm. Additionally, the latter actor revealed a relatively higher increment in produced particles in the maximum region. Two HU tables with different greyscale subdivisions were explored, namely the HU scale from the TP system RayStation and the default HU scale from GATE. The R80 and R50 values, were compared with the calculated TP in order to analyse the range uncertainties in distal and lateral direction of the beam. The evaluated R80 and R50 values in lateral and distal direction of the beam, in relation to the depth dose distribution, were below 3 mm. Other publications like Parodi et.al. and Knopf et.al., revealed deviations of approximately 13mm. The HU scale from the TP system Raystation, compared to the HU scale from GATE, showed lower deviations. In distal and lateral direction the range uncertainty was approximately 0.5 mm lower. This states that HU scales with a greater greyscale subdivision produces more accurate results. With the final simulation parameters, dose and activity distributions of an irradiated prostate case were visually compared with the calculated TP and the literature. Similarities for the activity distributions were found, but also irregularities, resulting from the export of the Digital Imaging and Communications in Medicine (DICOM) files with RayStation to GATE. In conclusion the improvement of MC simulations has the potential in PT-PET to increase the prediction and verification of beam applications with +activity distributions in clinical based ion beam therapy. Further simulations are necessary to investigate the behaviour and influence of different simulation parameters in GATE on the reliability of the simulations.