5. One-Dimensional Diffusion Processes
Henry C. Tuckwell · Society for Industrial and Applied Mathematics eBooks · 1989
The functional differential equations that arise from Stein's model are, as we saw in the previous chapter, difficult or cumbersome to solve. When the discontinuous Markov processes are replaced by approximating diffusions, the corresponding equations are differential equations for which there is a large body of literature in regard to both analytical and numerical methods of solution. In this chapter we introduce the well-known Wiener and Ornstein—Uhlenbeck processes as representatives of the state of a neuron. We also consider the less studied diffusion which arises when reversal potentials are employed, and we briefly consider the relevant weak convergence results which have only recently been obtained.