A stochastic differential equation. More...

Inheritance diagram for DifferentialEquation:

Public Member Functions
	DifferentialEquation (double x0, double dx0, const string &name="", const string &type="Differential Equation")
	starting value More...

	DifferentialEquation (Time *time, double x0, double dx0, const string &name="", const string &type="Differential Equation")
	Construct. More...

	DifferentialEquation (const string &name="", const string &type="Differential Equation")
	Construct. More...

virtual	~DifferentialEquation ()
	Destroy.

virtual void	prepareNextState ()
	Calculate value for next time step. More...

virtual void	init (double x0)
	Sets value to a starting value. More...

virtual void	init ()
	Sets value to starting value.

double	getStartingValue () const
	Get the starting value.

int	addTerm (StochasticFunction integrand, StochasticVariable integrator)
	Add term. More...

void	rmTerm (int n)
	Remove term. More...

void	setTerm (int n, StochasticFunction integrand, StochasticVariable integrator)
	Set term. More...

int	getNTerms () const
	Get number of terms. More...

StochasticFunction *	getIntegrand (int n)
	Get integrand part of a term. More...

StochasticVariable *	getIntegrator (int n)
	Get integrator part of a term. More...

virtual string	getParameter (const string &name) const
	Get parameter. More...

void	setParameter (const string &name, const string &value)
	Set parameter. More...

bool	isIto () const
	Is integration mode Ito?

bool	isStratonovich () const
	Is integration mode Stratonovich?

void	setIto ()
	Set integration mode to Ito.

void	setStratonovich ()
	Set integration mode to Stratonovich.

Public Member Functions inherited from StochasticVariable
	StochasticVariable (class Time *time, const string &name="", const string &type="Stochastic Variable")
	Create.

double	operator() ()
	Returns the value at the current time step. More...

double	d ()
	Returns the increment at the current time step. More...

Public Member Functions inherited from StochasticProcess
	StochasticProcess (class Time *time, const string &name="", const string &type="Stochastic")
	Create.

virtual	~StochasticProcess ()
	Destroy.

virtual void	proceedToNextState ()
	Proceed one time step. More...

bool	isNextStatePrepared ()
	Whether.

virtual double	getIncrement ()
	Returns the increment. More...

virtual double	getCurrentValue ()
	Returns the value of the process. More...

virtual double	getNextValue ()
	Returns the next value of the process. More...

virtual void	setNextValue (double d)
	Set the next value of the process. More...

virtual void	setCurrentValue (double d)
	Set the current value of the process. More...

void	setDescription (string s)
	Set stochastic description.

string	getDescription ()
	Get the name. More...

Public Member Functions inherited from Parametric
string	getType () const
	Type of object.

string	getName () const
	Name of object.

void	setName (const string &name)
	Name of object.

string	getConfiguration () const
	Returns the configuration of the object. More...

string	getAllParameters () const
	String with all parameter settings.

void	addParameter (const string &name)
	Add a parameter. More...

void	rmParameter (const string &name)
	Remove a parameter. More...

Public Member Functions inherited from TimeDependent
	TimeDependent (class Time *time)
	Construct. More...

virtual class Time *	getTime () const
	Return pointer to the time object.

Public Member Functions inherited from Physical
	Physical ()
	Construct.

	Physical (const Physical &)
	Copy.

	Physical (string name)
	Construct.

	Physical (string name, string unitPrefix, string unitSymbol)
	Construct.

	Physical (string name, Unit unit)
	Construct.

virtual string	getPhysicalDescription ()
	Returns the physical description. More...

virtual string	getUnitName ()
	Returns the unit name.

virtual string	getUnitSymbol ()
	Returns the unit name.

virtual void	setPhysicalDescription (string name)
	Set the name. Same as setDescription(). More...

virtual void	setUnit (Unit u)
	Set the unit.

virtual void	setUnitPrefix (int n)
	Set unit prefix. More...

virtual Unit	getUnit () const
	Retrieve the unit.

Public Attributes
void(DifferentialEquation::*	eqnMethodPtr )()
	Member pointer to one of the privat fcns.

Additional Inherited Members
Protected Member Functions inherited from Parametric
	Parametric (const string &name, const string &type)
	Create object of type and name.

virtual	~Parametric ()
	Destroy object.

Protected Attributes inherited from StochasticProcess
double	stochCurrentValue
	the current value

double	stochNextValue
	the next value (direct future)

bool	stochNextStateIsPrepared
	whether prepareNextState() was successful

string	stochDescription
	the name of the quantity

Detailed Description

A stochastic differential equation.

Class implementing stochastic differential equations (SDEs). Ito- and Stratonovich integrals can be chosen, integrators and integrands can be added at runtime.

This class implements stochastic differential equations (SDEs) of the form

$dX = \sum_i f_i(X) dY_i$

(using It\^o integrals), or

$dX = \sum_i f_i(X) \circ dY_i$

(using Stratonovich integrals). The sum goes over multiple different functions $f_i$ . These should be intepreted as integral equations of the form

$X - X_0 = \sum_i \intop f_i(X) dY_i$

(Ito), or

$X - X_0 = \sum_i \intop f_i(X) \circ dY_i$

(Stratonovich). It\^o mode can be set by calling setIto(), Stratonovich mode can be set by calling setStratonovich(). Which mode is used can be tested by querying isIto() (true if Ito mode) or isStratonovich() (true if Stratonovich integrals are used). At the moment there is only the 0.5-strong-order Euler scheme implemented, but Milstein and Taylor of higher order are planned for the future. See the main page for display of the error made when integrating. Here is a short example of the difference of Ito and Stratonovich integration (the equation is $dX_t = aX_tdt + bX_tdW_t$ or $dX_t = aX_tdt + bX_t\circ dW_t$ with $a=-8.0$ and $b=0.8$ .):

The integrands $f_i(X_t)$ are objects of the type Integrand, and the integrators $dY_i$ are objects of the type Integrator. They are stored in arrays of function objects, and their Integrand::operator()(double) or Integrator::operator()() are called each time proceedToNextState() is called. Use dGetValue() (from StochVar) or operator(double) to get the current value of the integral. The function proceedToNextState() must be used to calculate the values of the next time step, the function prepareNextState() must be used to update the object. New integrators and integrands may be added easily by calling nAddIntegrator() or nAddIntegrand().

DifferentialEquation itself is of type Integrator and of type Integrand, so complex cascades of differential equations may be implemented. If you have a complex network of interdependent SDEs, you must first call the proceedToNextState() function of all objects, then the prepareNextState() function of all objects. Otherwise circular dependencies will not get updated correctly.

Constructor & Destructor Documentation

DifferentialEquation::DifferentialEquation	(	double	x0,
		double	dx0,
		const string &	name = `""`,
		const string &	type = `"Differential Equation"`
	)

starting value

Construct.

Parameters

x0	starting value
dx0	starting increment
name	object name
type	object type

DifferentialEquation::DifferentialEquation	(	Time *	time,
		double	x0,
		double	dx0,
		const string &	name = `""`,
		const string &	type = `"Differential Equation"`
	)

Construct.

Parameters

time	global time object
x0	starting value
dx0	starting increment
name	object name
type	object type

DifferentialEquation::DifferentialEquation	(	const string &	name = `""`,
		const string &	type = `"Differential Equation"`
	)

inline

Construct.

The same as using DifferentialEquation(0.0, 0.0).

Parameters

name	object name
type	object type

Member Function Documentation

int DifferentialEquation::addTerm	(	StochasticFunction *	integrand,
		StochasticVariable *	integrator
	)

Add term.

Returns: index of new term

Parameters

integrator integrand part of term integrator part of term

StochasticFunction* DifferentialEquation::getIntegrand ( int n )

Get integrand part of a term.

Parameters

n	index of term

StochasticVariable* DifferentialEquation::getIntegrator ( int n )

Get integrator part of a term.

Parameters

n	index of term

int DifferentialEquation::getNTerms ( ) const

inline

Get number of terms.

Returns: number of terms in differential equation

virtual string DifferentialEquation::getParameter ( const string & name ) const

virtual

Get parameter.

In a derived class, override this to handle every parameter you implement. If a parameter is described using multiple strings separated by space, this indicates a parameter of a parameter.

Parameters

name	name of parameter

Reimplemented from Parametric.

virtual void DifferentialEquation::init ( double x0 )

virtual

Sets value to a starting value.

Parameters

x0	starting value

virtual void DifferentialEquation::prepareNextState ( )

virtual

Calculate value for next time step.

This just calculates the next value. Nothing is changed before proceedToNextState() is called.

Reimplemented from StochasticProcess.

void DifferentialEquation::rmTerm ( int n )

Remove term.

Parameters

n	index of term

void DifferentialEquation::setParameter	(	const string &	name,
		const string &	value
	)

virtual

Set parameter.

In a derived class, override this to handle every parameter you implement. If a parameter is described using multiple strings separated by space, this indicates a parameter of a parameter.

Parameters

name	name of parameter
value	value of parameter

Reimplemented from Parametric.

void DifferentialEquation::setTerm	(	int	n,
		StochasticFunction *	integrand,
		StochasticVariable *	integrator
	)

Set term.

Parameters

n	index of term
integrator	integrand part of term integrator part of term

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation