OrnsteinUhlenbeckProcess

OrnsteinUhlenbeckProcess[μ,σ,θ]

represents a stationary OrnsteinUhlenbeck process with long-term mean μ, volatility sigma, and mean reversion speed θ.

OrnsteinUhlenbeckProcess[μ,σ,θ,x0]

represents an OrnsteinUhlenbeck process with initial condition x0.

Details

Examples

open allclose all

Basic Examples  (3)

Simulate an OrnsteinUhlenbeck process with a random initial condition:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

With fixed initial condition:

In[3]:=
Click for copyable input
In[4]:=
Click for copyable input
Out[4]=

Mean and variance functions:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

With fixed initial condition:

In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
Out[4]=

Covariance function:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

With fixed initial condition:

In[3]:=
Click for copyable input
Out[3]=
In[4]:=
Click for copyable input
Out[4]=

Scope  (12)

Generalizations & Extensions  (1)

Properties & Relations  (9)

Neat Examples  (3)

See Also

WienerProcess  GeometricBrownianMotionProcess  BrownianBridgeProcess  NormalDistribution

Introduced in 2012
(9.0)