Tensorial products of functional ARMA processes

We study the structure of tensorial products for the autoregressive and moving average processes (Xn)(Xn), with values in a Hilbert space HH and with innovations that are martingale differences.The obtained models are ARMA(H⊗H)ARMA(H⊗H) processes, possibly non standard. We provide criteria for the standardness of these models, we specify the results in the real case, give some examples and consider some applications.