Comparison of stochastic processes by Markov projection and functional Itô calculus Abstract: In this thesis a systematic approach to the comparison of stochastic processes is pursued. In particular the classes of Markov processes and semimartingales are considered. Comparison results for the one dimensional marginals of Markov processes are established and then transferred to semimartingales by the method of Markov projections. Also a direct comparison of one dimensional marginals of general semimartingales is accomplished. This then is generalized to more dimensional marginals by functional Itô calculus