In this chapter, for the convenience of exposition, we remind some basic notions of stochastic calculus and mathematical statistics. It is supposed that the reader is familiar with stochastic calculus; therefore, the properties of the stochastic integral, the likelihood ratio formula, and limit theorems are given without proofs. The definitions and properties of some estimators of the parameters are given in more detail because they are less well-known. The Kalman–Bucy filter is provided with the proof due to the importance of this result for the problems considered in this work. At the end, some lower bounds on the mean-squared risks are presented and the possibility of the construction of a lower bound in the problem of adaptive filtering is discussed.