Limiting connection between discrete and continuous time forward interest rate curve models

We study discrete time Heath-Jarrow-Morton (HJM) type of interest rate curve models, where the forward interest rates - in contrast to the classical HJM models - are driven by a random field. Our main aim is to investigate the relationship between the discrete time forward interest rate curve model and its continuous time counterpart. We derive a general result on the convergence of discrete time models and we give special focus on the nearly unit root spatial autoregression model