Linear models of noisy signals with continuous and discrete time have been characterized, along with their respective identification characteristics. An analysis of the properties of random processes with independent increments and infinitely divisible white noise has been conducted. The concept of a linear random process is defined, and an analysis of its probability properties using characteristic functions is provided. It is shown that linear random processes have infinitely divisible distributions. Additionally, it is proven that linear random processes exhibit ergodicity and mixing properties, which are crucial for identification tasks. Linear random processes are closely related to models of colored noise. Properties and identification characteristics of the most important multidimensional linear models are also discussed. This includes the vector linear random process and the scalar spatiotemporal linear random field. Conditional linear random processes are defined as stochastic integrals of a random kernel with a process of independent increments. Expressions for multidimensional characteristic functions and moment functions for this class of models are derived. Conditions for the conditional linear random process to be stationary are described.