Gaussian channels and the optimal coding

For the Gaussian channel Y(t) = [Phi]([xi](s), Y(s); s [less, double equals] t) + X(t), the mutual information I([xi], Y) between the message [xi](·) and the output Y(·) is evaluated, where X(·) is a Gaussian noise. Furthermore, the optimal coding under average power constraints is constructed.Gaussian channel mutual information canonical representation of Gaussian processes reproducing kernel Hilbert space optimal coding

Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions

The central limit (or fluctuation) phenomena are discussed in the interacting diffusion system. The tightness in the Kolmogorov-Prokhorov sense is proved for a sequence of distribution valued processes arising from finite particle systems. Further, the stochastic differential equation for the limit process is derived by constructing an infinite dimensional Brownian motion.central limit theorem fluctuation interacting diffusion system infinite dimensional process