Table 1: Various kernels and their induced covariance functions in the two-dimensional plane.

Kernel Covariance function
K( t ) α Exp( 1/ 2 t 2 ) C( d )α Exp( 1/ 2 d/ 2 2 )
K( t ) α I[ t < 1/2 ] C( d )α Exp( d )
K( t ) α  ( 1 t 3 / s 3 ) 3 I[ t<s ] C( d )α ( 13/ 2 d +1/ 2 d 3 )I[ d<1 ]