Schematic illustration of the stochastic shielding approximation, for a graph representing 24 transitions (directed edges) interconnecting eight states (vertices).

<p>One of the states (black disk) is distinguishable from the rest (white disks). For example, the black disk could represent a conducting ion channel state, while the white disks could represent non-conducting states. <b>Left:</b> Numerical simulation of the full process is computationally expensive: each blue trace superimposed on an edge represents independently generated stochastic forcing, but not all edges make significant contributions to fluctuations in the state of interest. <b>Right:</b> Rather than simulate the full process, the stochastic shielding approximation reduces the number of independent noise sources (blue edges) used to drive the stochastic process on the graph, while preserving the dynamical behavior of a particular projection of the random process.