We present telescoping recursive representations for both continuous and discrete indexed noncausal Gauss-Markov random fields. Our recursions start at the boundary (for example, a hypersurface in R, d ≥ 1) and telescope inwards. Under appropriate conditions, the recursions for the random field are differential/difference representations driven by white noise, for which we can use standard recu...

We develop a physical analogy for the Kalman-Bucy filter, in which the partially observed signal describes a statistical mechanical system interacting with a heat bath. The ‘universe’ comprising this system and the heat bath obeys a non-decrease law of entropy similar to the Second Law of Thermodynamics. However, this law can be violated in the presence of partial observations. Like Maxwell’s d...