Stationarity in Stochastic Processes

This lecture delves into the concept of stationarity in stochastic processes, exploring how the statistical characteristics of processes remain constant over time. The instructor explains the conditions for weak and strict stationarity, illustrating with examples how processes can exhibit different levels of stationarity. Through detailed calculations and explanations, the lecture covers the implications of stationarity on the correlation between random variables and the Fourier transform. The instructor demonstrates how to determine stationarity using characteristic functions and highlights the distinction between deterministic and random fluctuations over time. The lecture concludes by hinting at future topics, such as ergodicity and empirical averages.