Contribution to Chapter One of Book Motivation for Using Jump Processes in Neurobiological Modeling Sprang Primarily

The observed electrical potentials of neurons as determined either by extracellular or intracellular recording are never constant. The same is true for grossly recorded field potentials and brain recordings such as the electroencephalogram. Often such recordings of potential exhibit quite sudden changes or jumps. If the sample paths of a continuous time random process have discontinuities then it is called a jump process. A process may be a pure jump process, like a Poisson process or a random walk, or there may be drift and or diffusion between the jumps.