There are only a few textbooks and monographs on random differential equations. This small book was published by Technical University of Poznań in the series of lecture notes for post-graduate studies. It is devoted to initial value problems for random differential equations. Contents: 1. Introduction. 2. Preliminaries. 3. Collection of trajectories as a solution of a random differential equation. 4. Second- order random processes. 5. Mean square solutions of random differential equations.
Before studying random equations, the author gives a survey of basic concepts of probability theory. Special attention is paid to random processes and to the mean square stochastic calculus. The author discusses two main approaches to the analysis of random differential equations: sample approach and mean square approach. Besides the existence and uniqueness of solutions, he is interested in solution techniques and applications. Generally, theorems are given without proofs, except in the chapter on second-order processes. The author refers for proofs to textbooks on probability theory, and to the monographs of H. Bunke [Gewöhnliche Differentialgleichungen mit zufälligen Parametern. (1972; Zbl 0243.60006)] and T. T. Soong [Random differential equations in science and engineering. (1973; Zbl 0348.60081)]. The book contains a large number of examples. Among them, random differential equations with complete solutions are the most interesting.