Tensorial products of functional ARMA processes

We study the structure of tensorial products for the autoregressive and moving average processes ( X n ) , with values in a Hilbert space H and with innovations that are martingale differences. tained models are A R M A ( 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.