Covariance Function for Processes

A discrete-time and discrete-state random process.

 In[1]:= XCovarianceFunction[BinomialProcess[1/3], s, t]
 Out[1]=
 In[2]:= XCovarianceFunction[BinomialProcess[1/3], s, t]; DiscretePlot3D[%, {s, 0, 10}, {t, 0, 10}, ExtentSize -> 1/2, ColorFunction -> "Rainbow", ImageSize -> Medium, AxesLabel -> Automatic]
 Out[2]=

A discrete-time and continuous-state random process.

 In[3]:= XCovarianceFunction[ARProcess[{2/3}, 1], s, t]
 Out[3]=
 In[4]:= XCovarianceFunction[ARProcess[{2/3}, 1], s, t]; DiscretePlot3D[%, {s, 0, 10}, {t, 0, 10}, ExtentSize -> 1/2, ColorFunction -> "Rainbow", ImageSize -> Medium, AxesLabel -> Automatic]
 Out[4]=

A continuous-time and discrete-state random process.

 In[5]:= XCovarianceFunction[PoissonProcess[1], s, t]
 Out[5]=
 In[6]:= XCovarianceFunction[PoissonProcess[1], s, t]; Plot3D[%, {s, 0, 10}, {t, 0, 10}, Mesh -> None, ColorFunction -> "Rainbow", ImageSize -> Medium, AxesLabel -> Automatic]
 Out[6]=

A continuous-time and continuous-state random process.

 In[7]:= XCovarianceFunction[OrnsteinUhlenbeckProcess[0, 1, 1/5], s, t]
 Out[7]=
 In[8]:= XCovarianceFunction[OrnsteinUhlenbeckProcess[0, 1, 1/5], s, t]; Plot3D[%, {s, 0, 10}, {t, 0, 10}, Mesh -> None, ColorFunction -> "Rainbow", ImageSize -> Medium, AxesLabel -> Automatic]
 Out[8]=