Module handling samples of Wiener processes (Brownain sample paths) The sample path is stored in a type Wiener_process_sample_path. The time grid use is stored in reversed order, i.e. the starting-time is stored in the last occupied element of the time vector, while the end-time is stored in the first element. This ordering optimizes the use within Monte Carlo codes with adaptive time stepping, in which you often wish to refine the next upcoming time step. With the reversed ordering the "next upcoming time step" is at the end of the vector, thus adding a time point will only require changes to the last few elements of the time-vectors. More...

Data Types
type	Wiener_process_sample_path
	Samples from the Wiener process. More...
Public Member Functions
subroutine	constructor_Wiener_process_sample_path (samplePath, Nelements, time1, time2, rand_normal_distribution)
	Constructor for the type Wiener_process_sample_path.
subroutine	destructor_Wiener_process_sample_path (samplePath)
	Destructor for the type Wiener_process_sample_path.
subroutine	add_point_on_sample_path (samplePath, new_time, rand_normal_distribution)
	Add point on the sample path by sampling a Brownian bridge.
subroutine	add_point_on_sample_path_index_k (k, samplePath, new_time, rand_normal_distribution)
	Add point at index `k` in the sample path, by sampling a Brownian bridge.
subroutine	remove_N_points_from_sample_path (samplePath, Nr_points_to_remove)
	Remove the `N` first points in the sample path.
real(8) function	Brownian_bridge (t0, t1, W0, W1, tn, rand_normal_distribution)
	Generate a point in the sample path of a Wiener process, under the condition of knowing the value of the Wiener process at both the "past" time `t0` and the future time `t1`.
subroutine	extendVectorAllocation (v, Nextra)
	Extend the memory allocation for the vector `v` by `Nextra` elements.
subroutine	test_sample_path
	Program for testing RFOF_Brownian_sample_paths module.

Detailed Description

Module handling samples of Wiener processes (Brownain sample paths) The sample path is stored in a type Wiener_process_sample_path. The time grid use is stored in reversed order, i.e. the starting-time is stored in the last occupied element of the time vector, while the end-time is stored in the first element. This ordering optimizes the use within Monte Carlo codes with adaptive time stepping, in which you often wish to refine the next upcoming time step. With the reversed ordering the "next upcoming time step" is at the end of the vector, thus adding a time point will only require changes to the last few elements of the time-vectors.

Use in Monte Carlo code for time-stepping:

Initialise sample path constructor_Wiener_process_sample_path, which will give you a sample path with a start and end point.
If you need to refine the time stepping, i.e. add time points to the sample path, use add_point_on_sample_path. Note that the new time has to occure after the start point of the sample path.
Once you have completed a part of the stepping you can remove the used time-points using remove_N_points_from_sample_path.

The next time step and step in the Wiener process are given by:

          dt = samplePath%time(  samplePath%Nr_stored_points-1) - samplePath%time(  samplePath%Nr_stored_points)
          dW = samplePath%Wiener(samplePath%Nr_stored_points-1) - samplePath%Wiener(samplePath%Nr_stored_points)

Author:: T. Johnson

Date:: 2010.08.28

Version:: "$Id: RFOF_wiener_sample_paths.F90 188 2011-09-12 11:50:22Z tjohnson $"

Definition at line 32 of file RFOF_wiener_sample_paths.F90.

Member Function/Subroutine Documentation

subroutine RFOF_wiener_sample_paths::constructor_Wiener_process_sample_path	(	type(Wiener_process_sample_path), intent(inout)	samplePath,
		integer, intent(in)	Nelements,
		real(8), intent(in)	time1,
		real(8), intent(in)	time2,
		real(8), intent(in)	rand_normal_distribution
	)

Constructor for the type Wiener_process_sample_path.

INPUT

Parameters:

Nelements	Number of elements to allocate for the vectors.
time1	Time at start of sample path.
time2	Time at end of sample path.
rand_normal_distribution	Random number determining the end state of the sample path.

INPUT/OUTPUT

Parameters:

samplePath Sample path of a Wiener process (brownian motion).

Definition at line 64 of file RFOF_wiener_sample_paths.F90.

subroutine RFOF_wiener_sample_paths::destructor_Wiener_process_sample_path ( type(Wiener_process_sample_path), intent(inout) samplePath )

Destructor for the type Wiener_process_sample_path.

INPUT/OUTPUT

Parameters:

samplePath Sample path of a Wiener process (brownian motion).

Definition at line 106 of file RFOF_wiener_sample_paths.F90.

subroutine RFOF_wiener_sample_paths::add_point_on_sample_path	(	type(Wiener_process_sample_path), intent(inout)	samplePath,
		real(8), intent(in)	new_time,
		real(8), intent(in)	rand_normal_distribution
	)

Add point on the sample path by sampling a Brownian bridge.

INPUT

Parameters:

new_time	Time for new point in sample path.
rand_normal_distribution	Random number determining the new point in the sample path.

INPUT/OUTPUT

Parameters:

samplePath Sample path of a Wiener process (brownian motion).

Definition at line 127 of file RFOF_wiener_sample_paths.F90.

subroutine RFOF_wiener_sample_paths::add_point_on_sample_path_index_k	(	integer, intent(in)	k,
		type(Wiener_process_sample_path), intent(inout)	samplePath,
		real(8), intent(in)	new_time,
		real(8), intent(in)	rand_normal_distribution
	)

Add point at index k in the sample path, by sampling a Brownian bridge.

INPUT

Parameters:

k	Index `k` at which the new sample should be added.
new_time	Time for new point in sample path.
rand_normal_distribution	Random number determining the new point in the sample path.

INPUT/OUTPUT

Parameters:

samplePath Sample path of a Wiener process (brownian motion).

Definition at line 186 of file RFOF_wiener_sample_paths.F90.

subroutine RFOF_wiener_sample_paths::remove_N_points_from_sample_path	(	type(Wiener_process_sample_path), intent(inout)	samplePath,
		integer, intent(in)	Nr_points_to_remove
	)

Remove the N first points in the sample path.

INPUT

Parameters:

Nr_points_to_remove Number of point to be remove in the begnning the sample path

INPUT/OUTPUT

Parameters:

samplePath Sample path of a Wiener process (brownian motion).

Definition at line 240 of file RFOF_wiener_sample_paths.F90.

real(8) function RFOF_wiener_sample_paths::Brownian_bridge	(	real(8), intent(in)	t0,
		real(8), intent(in)	t1,
		real(8), intent(in)	W0,
		real(8), intent(in)	W1,
		real(8), intent(in)	tn,
		real(8), intent(in)	rand_normal_distribution
	)

Generate a point in the sample path of a Wiener process, under the condition of knowing the value of the Wiener process at both the "past" time t0 and the future time t1.

Parameters:

t0	Time at of point in sample path
t1	Time at previous point in sample path
W0	Value of Wiener process at time `t0`
W1	Value of Wiener process at time `t1`
rand_normal_distribution	Random number determining the new point in the sample path.
tn	Time at new point to be added to sample path

Returns:: Wn New sample from the Brownian path.

Definition at line 266 of file RFOF_wiener_sample_paths.F90.

subroutine RFOF_wiener_sample_paths::extendVectorAllocation	(	real(8), dimension(:), intent(inout), pointer	v,
		integer, intent(in)	Nextra
	)

Extend the memory allocation for the vector v by Nextra elements.

INPUT

Parameters:

Nextra Number of point to add to the vector v.

INPUT/OUTPUT

Parameters:

v	Vector of real number; the length of this vector should be extended by `Nextra` elements.

Definition at line 299 of file RFOF_wiener_sample_paths.F90.

subroutine RFOF_wiener_sample_paths::test_sample_path ( )

Program for testing RFOF_Brownian_sample_paths module.

Output to expect:

  path after constructor           2           3           3
    2.0000000000000000        1.0000000000000000     
    1.0000000000000000        0.0000000000000000     
  new samplePath%Nr_stored_points:           3
  1 point added           3           3           3
    2.0000000000000000        1.3999999999999999        1.0000000000000000     
    1.0000000000000000       0.13599999999999990        0.0000000000000000     
  new samplePath%Nr_stored_points:           4
  2 point added           4           6           6
    2.0000000000000000        1.8000000000000000        1.3999999999999999        1.0000000000000000     
    1.0000000000000000       0.81066666666666676       0.13599999999999990        0.0000000000000000     
  new samplePath%Nr_stored_points:           5
  3 point added           5           6           6
    2.0000000000000000        1.8000000000000000        1.8000000000000000        1.3999999999999999        1.0000000000000000     
    1.0000000000000000       0.81066666666666676       0.81066666666666676       0.13599999999999990        0.0000000000000000     
  new samplePath%Nr_stored_points:           5
  3 point added           5           6           6
    2.0000000000000000        1.8000000000000000        1.8000000000000000        1.8000000000000000        1.3999999999999999     
    1.0000000000000000       0.81066666666666676       0.81066666666666676       0.81066666666666676       0.13599999999999990     
  Error in add_point_on_sample_path:
  Attempting to add point before the start of the Wiener process
  ABORT

Definition at line 355 of file RFOF_wiener_sample_paths.F90.

The documentation for this module was generated from the following file:

RFOF_wiener_sample_paths.F90

Data Types

Public Member Functions

Detailed Description

Member Function/Subroutine Documentation