The main topic of this work is the statistical analysis of single-electron transport through quantum dot systems coupled to electronic leads via tunneling barriers. With the development of highly sensitive charge detectors, it has become possible to resolve the charge of such systems with single-electron precision in real time and record it in the form of a random telegraph signal. To extract valuable information about the fundamental processes of the quantum system from the measured signal, we use two methods for statistical analysis: full counting statistics and waiting times.

Prior to this, we contribute to the theoretical description of the dynamics of strongly interacting open quantum systems. By using the real-time diagrammatic technique, we derive a generalized master equation. To cast the equation into Lind- blad form, we introduce the coherent approximation as an improved alternative to the secular approximation.

Then, we come to the heart of this work and develop a theoretical model for measurement errors that inevitably occur in any measured telegraph signal. These include systematic errors due to a finite time resolution and a noisy signal, and statistical errors due to a limited measurement time. The model can be used to faithfully account for the influence of such measurement imperfections.

We find that in particular factorial cumulants are extremely robust to errors. This general error resilience is confirmed by both our error model and experimental data of charge fluctuations in a quantum dot.

We then perform a statistical analysis of single-electron transport for a variety of systems. First, we examine experimental data on the Auger effect in an optically driven self-assembled quantum dot. Using full counting statistics and waiting times, we are able to infer internal spin dynamics from the analysis of charge fluctu- ations alone. In particular, we find that the spin in the magnetic field is optically pumped to the higher energy state.

Subsequently, we analyze correlations in electron transport, which can be re- vealed by a violated sign criterion for factorial cumulants. We study two systems that have already been experimentally realized: a quantum dot with attractive in- teraction and a quantum dot in which electrons can be coherently trapped in a dark state. Both systems leave unique signatures in the electron transport, which can be indicated by factorial cumulants.

Finally, we present the effect of synchronized coherent charge oscillations when two double quantum dots are capacitively coupled. We demonstrate that the fingerprint of this effect in electron transport can be visualized by using waiting times.