FKG inequality for Levy processes and SDE

The Fortuin-Kasteleyn-Ginibre inequality is a famous correlation inequality in measure theory. In this thesis our goal is to provide sufficient conditions for the validity of the FKG inequality in probabilistic contexts. We will begin by discussing the FKG inequality for continuous Brownian motion and present some condition under which the FKG inequality holds for solutions of stochastic differential equations, subsequently we present a necessary and sufficient condition for the positive correlation of the Levy processes and a sufficient condition for the positive correlation of some Markov chains.