program main !*****************************************************************************80 ! !! ornstein_uhlenbeck_test() tests ornstein_uhlenbeck(). ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 18 January 2013 ! ! Author: ! ! John Burkardt ! implicit none call timestamp ( ) write ( *, '(a)') ' ' write ( *, '(a)' ) 'ornstein_uhlenbeck_test():' write ( *, '(a)' ) ' FORTRAN90 version.' write ( *, '(a)' ) ' Test ornstein_uhlenbeck().' call ou_euler_test ( ) call ou_euler_maruyama_test ( ) ! ! Terminate. ! write ( *, '(a)' ) '' write ( *, '(a)' ) 'ornstein_uhlenbeck_test:' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) '' call timestamp ( ) stop 0 end subroutine ou_euler_test ( ) !*****************************************************************************80 ! !! OU_EULER_TEST tests OU_EULER. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 18 January 2013 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) real ( kind = rk ) mu integer n real ( kind = rk ) sigma real ( kind = rk ) theta real ( kind = rk ) tmax real ( kind = rk ) x0 write ( *, '(a)' ) '' write ( *, '(a)' ) 'OU_EULER_TEST:' write ( *, '(a)' ) ' Estimate a solution to the Ornstein-Uhlenbeck equation' write ( *, '(a)' ) ' using the Euler method for stochastic differential equations.' write ( *, '(a)' ) '' theta = 2.0D+00 write ( *, '(a,g14.6)' ) ' Using decay rate THETA = ', theta mu = 1.0D+00 write ( *, '(a,g14.6)' ) ' Using mean MU = ', mu sigma = 0.15D+00 write ( *, '(a,g14.6)' ) ' Using variance SIGMA = ', sigma x0 = 2.0D+00 write ( *, '(a,g14.6)' ) ' Using initial value X0 = ', x0 tmax = 3.0D+00 write ( *, '(a,g14.6)' ) ' Using final time TMAX = ', tmax n = 10000 write ( *, '(a,i8)' ) ' Using number of timesteps N = ', n call ou_euler ( theta, mu, sigma, x0, tmax, n ) return end subroutine ou_euler_maruyama_test ( ) !*****************************************************************************80 ! !! OU_EULER_MARUYAMA_TEST tests OU_EULER_MARUYAMA. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 21 January 2013 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) real ( kind = rk ) mu integer n integer r real ( kind = rk ) sigma real ( kind = rk ) theta real ( kind = rk ) tmax real ( kind = rk ) x0 write ( *, '(a)' ) '' write ( *, '(a)' ) 'OU_EULER_MARUYAMA_TEST:' write ( *, '(a)' ) ' Estimate a solution to the Ornstein-Uhlenbeck equation' write ( *, '(a)' ) ' using the Euler-Maruyama method for stochastic ' write ( *, '(a)' ) ' differential equations.' write ( *, '(a)' ) '' theta = 2.0D+00 write ( *, '(a,g14.6)' ) ' Using decay rate THETA = ', theta mu = 1.0D+00 write ( *, '(a,g14.6)' ) ' Using mean MU = ', mu sigma = 0.15D+00 write ( *, '(a,g14.6)' ) ' Using variance SIGMA = ', sigma x0 = 2.0D+00 write ( *, '(a,g14.6)' ) ' Using initial value X0 = ', x0 tmax = 3.0D+00 write ( *, '(a,g14.6)' ) ' Using final time TMAX = ', tmax n = 10000 write ( *, '(a,i6)' ) ' Using number of large timesteps N = ', n r = 16 write ( *, '(a,i6)' ) ' Using number small time steps per one large time step R = ', r call ou_euler_maruyama ( theta, mu, sigma, x0, tmax, n, r ) return end