Chapter 18 - Stochastic Processes

Abstract

In analyzing neural data, we often have to deal with quantities that fluctuate randomly in time. For example, an intracellular recording of the membrane potential of a neuron in vivo or a sequence of extracellular action potentials. Variables that fluctuate randomly in time are called stochastic processes or random functions. In this chapter, we define 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. We have already encountered the simplest such process in previous chapters in the form of the homogeneous Poisson and gamma renewal processes. Next, we introduce some of the tools used to study the properties of stochastic processes. In particular, we will see that the Fourier transform allows us to characterize the frequency content of stochastic processes through spectral analysis.