A stochastic kernel is the transition function of a (usually discrete) stochastic process. Often, it is assumed to be iid, thus a probability density function

Examples

• The uniform kernel is 1 / 2 for - 1 < t < 1.
• The triangular kernel is 1 - | t | for - 1 < t < 1.
• The quartic kernel is 15 / 26(1 - t²)² for - 1 < t < 1.
• The Epanechnikov kernel is 3 / 4(1 - t²) for - 1 < t < 1.

Often, the data is fitted to such a kernel by setting a window width h, considering only x_i's in and setting t_i = (x_i - x) / h.