The radio frequency transmitter is a key component in contemporary MIMO OFDM systems. A detailed study of a 2×2 MIMO transmitter subjected to correlated input data streams, nonlinear distortion, thermal noise, and crosstalk is provided by stochastic modeling. The effects of correlated input streams, crosstalk and nonlinearities are studied in detail, and exemplified both by approximate expressions and numerical simulations. Key results include exact and approximate expressions for the normalized mean-squared error (NMSE) for systems with or without digital predistortion, the relationship between NMSE and the signal-to-noise-and-distortion ratio, the properties of the distortion noise, and a novel design for power amplifier back-off for MIMO-transmitters subject to crosstalk. The theoretical derivations are illustrated by numerical examples and simulation results, and their relationship to state-of-the-art research are discussed. OAPA