CovarianceFunction[BinomialProcess[1/3],s,t]

DiscretePlot3D[%,{s,0,10},{t,0,10},ExtentSize->1/2,ColorFunction->"Rainbow",ImageSize->Medium,AxesLabel->Automatic]

CovarianceFunction[ARProcess[{2/3},1],s,t]

DiscretePlot3D[%,{s,0,10},{t,0,10},ExtentSize->1/2,ColorFunction->"Rainbow",ImageSize->Medium,AxesLabel->Automatic]

CovarianceFunction[PoissonProcess[1],s,t]

Plot3D[%,{s,0,10},{t,0,10},Mesh->None,ColorFunction->"Rainbow",ImageSize->Medium,AxesLabel->Automatic]

CovarianceFunction[OrnsteinUhlenbeckProcess[0,1,1/5],s,t]

Plot3D[%,{s,0,10},{t,0,10},Mesh->None,ColorFunction->"Rainbow",ImageSize->Medium,AxesLabel->Automatic]