Stochastic kernel

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

Formally a density can be

f_{\lambda}(y)=\frac{1}{I\lambda}\sum_{i=1}^{I}K\left(\frac{y-y_{i}}{\lambda}\right),

where yi is the observed series, λ is the bandwidth, and K is the kernel function.

[edit] Examples

  • The uniform kernel is K = 1 / 2 for − 1 < t < 1.
  • The triangular kernel is K = 1 − | t | for − 1 < t < 1.
  • The quartic kernel is K = (15 / 16)(1 − t2)2 for − 1 < t < 1.
  • The Epanechnikov kernel is K = (3 / 4)(1 − t2) for − 1 < t < 1.

[edit] External links

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