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According to the following reference page

http://reference.wolfram.com/language/ref/ItoProcess.html

The driving process dproc can be any process that can be converted to a standard Ito process

and

Processes proc that can be converted to standard ItoProcess form include OrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, StratonovichProcess, and ItoProcess.

However, it does not seem to work in my example as follows:

OUmodproc = ItoProcess[\[DifferentialD]x[t]ItoProcess[\[DifferentialD]x[
     t] == -x[t] \[DifferentialD]t + \[DifferentialD]w[t], 
        x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]]
(* ItoProcess[\[DifferentialD]x[ t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
 x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]] *)

RandomFunction[OUmodRandomFunction[proc, {0., 5., 0.01}]
ListLinePlot[%, Filling -> Axis]

During evaluation of In[33]:= RandomFunction::unsproc: The specification ItoProcess[\[DifferentialD]x[t]==\[DifferentialD]w[t]-\[DifferentialD]t x[t],x[t],{x,1},t,w\[Distributed]OrnsteinUhlenbeckProcess[0,1,1]] is not a random process recognized by the system.


(* RandomFunction[
 ItoProcess[\[DifferentialD]x[
     t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
  x[t], {x, 1}, t, 
  w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]], {0., 5., 0.01}] *)

which resulted in the error:

RandomFunction::unsproc: The specification ItoProcess[[DifferentialD]x[t]==[DifferentialD]w[t]-[DifferentialD]t x[t],x[t],{x,1},t,w[Distributed]OrnsteinUhlenbeckProcess[0,1,1]] is not a random process recognized by the system.

Note that in defining the ItoProcess proc like above, w \[Distributed] WienerProcess[0,1] would work, but w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1] does not.

According to the following reference page

http://reference.wolfram.com/language/ref/ItoProcess.html

The driving process dproc can be any process that can be converted to a standard Ito process

and

Processes proc that can be converted to standard ItoProcess form include OrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, StratonovichProcess, and ItoProcess.

However, it does not seem to work in my example as follows:

OUmod = ItoProcess[\[DifferentialD]x[t] == -x[t] \[DifferentialD]t + \[DifferentialD]w[t], 
        x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]]
(* ItoProcess[\[DifferentialD]x[ t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
 x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]] *)

RandomFunction[OUmod, {0., 5., 0.01}]
ListLinePlot[%, Filling -> Axis]

During evaluation of In[33]:= RandomFunction::unsproc: The specification ItoProcess[\[DifferentialD]x[t]==\[DifferentialD]w[t]-\[DifferentialD]t x[t],x[t],{x,1},t,w\[Distributed]OrnsteinUhlenbeckProcess[0,1,1]] is not a random process recognized by the system.


(* RandomFunction[
 ItoProcess[\[DifferentialD]x[
     t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
  x[t], {x, 1}, t, 
  w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]], {0., 5., 0.01}] *)

According to the following reference page

http://reference.wolfram.com/language/ref/ItoProcess.html

The driving process dproc can be any process that can be converted to a standard Ito process

and

Processes proc that can be converted to standard ItoProcess form include OrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, StratonovichProcess, and ItoProcess.

However, it does not seem to work in my example:

proc = ItoProcess[\[DifferentialD]x[
     t] == -x[t] \[DifferentialD]t + \[DifferentialD]w[t], 
  x[t], {x, 1}, t, 
  w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]]
RandomFunction[proc, {0., 5., 0.01}]
ListLinePlot[%, Filling -> Axis]

which resulted in the error:

RandomFunction::unsproc: The specification ItoProcess[[DifferentialD]x[t]==[DifferentialD]w[t]-[DifferentialD]t x[t],x[t],{x,1},t,w[Distributed]OrnsteinUhlenbeckProcess[0,1,1]] is not a random process recognized by the system.

Note that in defining the ItoProcess proc like above, w \[Distributed] WienerProcess[0,1] would work, but w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1] does not.

2 deleted 621 characters in body
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According to the following reference page

http://reference.wolfram.com/language/ref/ItoProcess.html

The driving process dproc can be any process that can be converted to a standard Ito process

and

Processes proc that can be converted to standard ItoProcess form include OrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, StratonovichProcess, and ItoProcess.

However, it does not seem to work in my example as follows:

In[32]:= OUmod = 
 ItoProcess[\[DifferentialD]x[
     t]ItoProcess[\[DifferentialD]x[t] == -x[t] \[DifferentialD]t + \[DifferentialD]w[t], 
        x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]]
 
Out[32]=(* ItoProcess[\[DifferentialD]x[
    t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
 x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]] *)

In[33]:= RandomFunction[OUmod, {0., 5., 0.01}]
ListLinePlot[%, Filling -> Axis]

During evaluation of In[33]:= RandomFunction::unsproc: The specification ItoProcess[\[DifferentialD]x[t]==\[DifferentialD]w[t]-\[DifferentialD]t x[t],x[t],{x,1},t,w\[Distributed]OrnsteinUhlenbeckProcess[0,1,1]] is not a random process recognized by the system.

Out[33]=
(* RandomFunction[
 ItoProcess[\[DifferentialD]x[
     t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
  x[t], {x, 1}, t, 
  w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]], {0., 5., 0.01}]] *)

According to the following reference page

http://reference.wolfram.com/language/ref/ItoProcess.html

The driving process dproc can be any process that can be converted to a standard Ito process

and

Processes proc that can be converted to standard ItoProcess form include OrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, StratonovichProcess, and ItoProcess.

However, it does not seem to work in my example as follows:

In[32]:= OUmod = 
 ItoProcess[\[DifferentialD]x[
     t] == -x[t] \[DifferentialD]t + \[DifferentialD]w[t], 
  x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]]
 
Out[32]= ItoProcess[\[DifferentialD]x[
    t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
 x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]]

In[33]:= RandomFunction[OUmod, {0., 5., 0.01}]
ListLinePlot[%, Filling -> Axis]

During evaluation of In[33]:= RandomFunction::unsproc: The specification ItoProcess[\[DifferentialD]x[t]==\[DifferentialD]w[t]-\[DifferentialD]t x[t],x[t],{x,1},t,w\[Distributed]OrnsteinUhlenbeckProcess[0,1,1]] is not a random process recognized by the system.

Out[33]= RandomFunction[
 ItoProcess[\[DifferentialD]x[
     t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
  x[t], {x, 1}, t, 
  w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]], {0., 5., 0.01}]

According to the following reference page

http://reference.wolfram.com/language/ref/ItoProcess.html

The driving process dproc can be any process that can be converted to a standard Ito process

and

Processes proc that can be converted to standard ItoProcess form include OrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, StratonovichProcess, and ItoProcess.

However, it does not seem to work in my example as follows:

OUmod = ItoProcess[\[DifferentialD]x[t] == -x[t] \[DifferentialD]t + \[DifferentialD]w[t], 
        x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]]
(* ItoProcess[\[DifferentialD]x[ t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
 x[t], {x, 1}, t, w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]] *)

RandomFunction[OUmod, {0., 5., 0.01}]
ListLinePlot[%, Filling -> Axis]

During evaluation of In[33]:= RandomFunction::unsproc: The specification ItoProcess[\[DifferentialD]x[t]==\[DifferentialD]w[t]-\[DifferentialD]t x[t],x[t],{x,1},t,w\[Distributed]OrnsteinUhlenbeckProcess[0,1,1]] is not a random process recognized by the system.


(* RandomFunction[
 ItoProcess[\[DifferentialD]x[
     t] == \[DifferentialD]w[t] - \[DifferentialD]t x[t], 
  x[t], {x, 1}, t, 
  w \[Distributed] OrnsteinUhlenbeckProcess[0, 1, 1]], {0., 5., 0.01}] *)
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