EulerDiscretization Class Reference

Euler discretization for stochastic processes. More...

#include <eulerdiscretization.hpp>

Inheritance diagram for EulerDiscretization:

Collaboration diagram for EulerDiscretization:

Public Member Functions
Array	drift (const StochasticProcess &, Time t0, const Array &x0, Time dt) const override
Real	drift (const StochasticProcess1D &, Time t0, Real x0, Time dt) const override
Matrix	diffusion (const StochasticProcess &, Time t0, const Array &x0, Time dt) const override
Real	diffusion (const StochasticProcess1D &, Time t0, Real x0, Time dt) const override
Matrix	covariance (const StochasticProcess &, Time t0, const Array &x0, Time dt) const override
Real	variance (const StochasticProcess1D &, Time t0, Real x0, Time dt) const override
Public Member Functions inherited from StochasticProcess::discretization
virtual	~discretization ()=default
virtual Array	drift (const StochasticProcess &, Time t0, const Array &x0, Time dt) const =0
virtual Matrix	diffusion (const StochasticProcess &, Time t0, const Array &x0, Time dt) const =0
virtual Matrix	covariance (const StochasticProcess &, Time t0, const Array &x0, Time dt) const =0
Public Member Functions inherited from StochasticProcess1D::discretization
virtual	~discretization ()=default
virtual Real	drift (const StochasticProcess1D &, Time t0, Real x0, Time dt) const =0
virtual Real	diffusion (const StochasticProcess1D &, Time t0, Real x0, Time dt) const =0
virtual Real	variance (const StochasticProcess1D &, Time t0, Real x0, Time dt) const =0

Detailed Description

Euler discretization for stochastic processes.

Definition at line 33 of file eulerdiscretization.hpp.

Member Function Documentation

drift() [1/2]

Array drift ( const StochasticProcess &  process, Time  t0, const Array &  x0, Time  dt  ) const

overridevirtual

Returns an approximation of the drift defined as $\mu(t_0, \mathbf{x}_0) \Delta t$.

Implements StochasticProcess::discretization.

Definition at line 24 of file eulerdiscretization.cpp.

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drift() [2/2]

Real drift ( const StochasticProcess1D &  process, Time  t0, Real  x0, Time  dt  ) const

overridevirtual

Returns an approximation of the drift defined as $\mu(t_0, x_0) \Delta t$.

Implements StochasticProcess1D::discretization.

Definition at line 30 of file eulerdiscretization.cpp.

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diffusion() [1/2]

Matrix diffusion ( const StochasticProcess &  process, Time  t0, const Array &  x0, Time  dt  ) const

overridevirtual

Returns an approximation of the diffusion defined as $\sigma(t_0, \mathbf{x}_0) \sqrt{\Delta t}$.

Implements StochasticProcess::discretization.

Definition at line 35 of file eulerdiscretization.cpp.

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diffusion() [2/2]

Real diffusion ( const StochasticProcess1D &  process, Time  t0, Real  x0, Time  dt  ) const

overridevirtual

Returns an approximation of the diffusion defined as $\sigma(t_0, x_0) \sqrt{\Delta t}$.

Implements StochasticProcess1D::discretization.

Definition at line 42 of file eulerdiscretization.cpp.

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covariance()

Matrix covariance ( const StochasticProcess &  process, Time  t0, const Array &  x0, Time  dt  ) const

overridevirtual

Returns an approximation of the covariance defined as $\sigma(t_0, \mathbf{x}_0)^2 \Delta t$.

Implements StochasticProcess::discretization.

Definition at line 47 of file eulerdiscretization.cpp.

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variance()

Real variance ( const StochasticProcess1D &  process, Time  t0, Real  x0, Time  dt  ) const

overridevirtual

Returns an approximation of the variance defined as $\sigma(t_0, x_0)^2 \Delta t$.

Implements StochasticProcess1D::discretization.

Definition at line 56 of file eulerdiscretization.cpp.

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