CHAPTER 16 - Stochastic Processes

Abstract

In analyzing neural data, one often has to deal with quantities that fluctuate randomly in time, like the intracellular membrane potential of a neuron recorded in vivo or a sequence of extracellular action potentials. Variables that fluctuate randomly in time are called stochastic processes or random functions. This chapter defines two types of stochastic processes that are used, respectively, to describe continuous variables, such as random potential fluctuations, and events, like random sequences of action potentials. The discussion delves into the characteristics of stochastic processes and introduces several examples that subsequently play a central role in the analysis of random fluctuations of continuous variables and discrete spike trains: the Wiener process, white noise, and the inhomogeneous Poisson process. Finally, the chapter studies the application of Fourier transforms to stochastic processes, which allow the characterization of their frequency content, a topic called spectral analysis.