This volume presents a mathematical treatment of classical inference theory (Neyman-Pearson, Fisher and Wald) from the perspective of using it in stochastic processes, including some generalizations. It includes analysis of likelihood ratios for both Gaussian and several other classes (infinitely divisible, jump Markov, diffusion and additive). Both linear and non-linear filtering (also for general non-quadratic criteria) are treated. The corresponding Kalman-Bucy filters for continuous parameter processes are presented. Consistency and limit distributions of estimations of biospectral densities of harmonizable processes are also included. The text is designed to be useful to researchers and graduate students working in mathematics, statistics, and systems and communication engineering.
