Class MilsteinSDE
- java.lang.Object
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- dev.nm.stat.stochasticprocess.univariate.sde.discrete.MilsteinSDE
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- All Implemented Interfaces:
DiscreteSDE
public class MilsteinSDE extends Object implements DiscreteSDE
Milstein scheme is a first-order approximation to a continuous-time SDE. It adds a term to the Euler scheme by expanding both the drift and diffusion terms to O(dt). \[ dX_t = \mu * dt + \sigma * \sqrt{dt} * Z_t + \frac{1}{2} \frac{d\sigma}{dt} * \sigma * dt * (Z_t^2 - 1) \]- See Also:
- Wikipedia: Milstein method
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Constructor Summary
Constructors Constructor Description MilsteinSDE(SDE sde)
Discretize a continuous-time SDE using the Milstein scheme.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
db(Ft ft)
\[ \frac{d\sigma}{dt} \]double
dXt(Ft ft)
This is the SDE specification of a stochastic process.Ft
getNewFt()
Get an empty filtration of the process.
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Constructor Detail
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MilsteinSDE
public MilsteinSDE(SDE sde)
Discretize a continuous-time SDE using the Milstein scheme.- Parameters:
sde
- a continuous-time SDE
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Method Detail
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dXt
public double dXt(Ft ft)
This is the SDE specification of a stochastic process. This is an implementation of the Milstein scheme. \[ dX_t = \mu * dt + \sigma * \sqrt{dt} * Z_t + \frac{1}{2} \frac{d\sigma}{dt} * \sigma * dt * (Z_t^2 - 1) \]- Specified by:
dXt
in interfaceDiscreteSDE
- Parameters:
ft
- a filtration- Returns:
- the increment of the process in
dt
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getNewFt
public Ft getNewFt()
Description copied from interface:DiscreteSDE
Get an empty filtration of the process.- Specified by:
getNewFt
in interfaceDiscreteSDE
- Returns:
- an empty filtration
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db
public double db(Ft ft)
\[ \frac{d\sigma}{dt} \]- Parameters:
ft
- a filtration- Returns:
- \(\frac{d\sigma}{dt}\)
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