Convert Parametric SDE Processes to Equivalent Ito Processes 

The canonical form of ItoProcess or StratonovichProcess in Mathematica encodes their defining SDEs as follows.

WienerProcess solves the SDE , where is the standard Wiener process, also known as the Brownian motion process.

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X ItoProcess[WienerProcess[\[Mu], \[Sigma]]]

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GeometricBrownianMotionProcess solves the SDE .

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X ItoProcess[ GeometricBrownianMotionProcess[\[Mu], \[Sigma], Subscript[x, 0]]]

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OrnsteinUhlenbeckProcess solves the SDE .

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X ItoProcess[ OrnsteinUhlenbeckProcess[\[Mu], \[Sigma], \[Theta], Subscript[x, 0]]]

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CoxIngersollRossProcess solves the SDE .

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X ItoProcess[ CoxIngersollRossProcess[\[Mu], \[Sigma], \[Theta], Subscript[x, 0]]]

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BrownianBridgeProcess solves the SDE .

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X ItoProcess[ BrownianBridgeProcess[\[Sigma], {Subscript[t, 1], Subscript[a, 1]}, {Subscript[t, 2], Subscript[a, 2]}]]

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