Implementations of the operator of conditional expectation with respect to gaussian distribution.
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This namespace contains different implementations of the class GaussRollback.
- See also
- IGaussRollback and GaussRollback
Implements the operator of conditional expectation with respect to gaussian distribution by an explicit finite difference scheme. The scheme is constructed so that the center weight is as close to zero as possible.
- Returns
- Implemenation of GaussRollback by means of binomial explicit finite difference scheme.
Returns the implementation of the operator of conditional expectation with respect to gaussian distribution by means of the Crank and Nicolson finite difference scheme.
- Parameters
-
rVarStep | This functions determines the number of steps in the scheme by the formula dVar/ (rVarStep(dH), where dVar is the variance of distribution. |
- Returns
- Implementation of GaussRollback by means of Crank-Nicolson scheme.
Returns the implementation of the operator of conditional expectation with respect to gaussian distribution by means of the Crank and Nicolson finite difference scheme.
- Parameters
-
dVarStepCoeff | This number determines the number of steps in the scheme by the formula dVar/ (dVarStepCoeff*dH), where dVar is the variance of distribution and dH is the step on the grid. |
- Returns
- Implementation of GaussRollback by means of Crank-Nicolson scheme.
Implements the operator of conditional expectation with respect to gaussian distribution by an implicit finite difference scheme.
- Parameters
-
rVarStep | This functions determines the number of steps in the scheme by the formula dVar/ (rVarStep(dH), where dVar is the variance of distribution. |
- Returns
- Implementation of GaussRollback by means of a implicit finite difference scheme.
Implements the operator of conditional expectation with respect to gaussian distribution by an implicit finite difference scheme.
- Parameters
-
dVarStepCoeff | This number determines the number of steps in the scheme by the formula dVar/ (dVarStepCoeff*dH*dH), where dVar is the variance of distribution and dH is the step on the grid. |
- Returns
- Implementation of GaussRollback by means of a implicit finite difference scheme.
Returns the implementation of the operator of conditional expectation with respect to gaussian distribution by means of sequential application of three schemes. First, we use explicit scheme with equal weights. This scheme efficiently handles possible discontinuities of input functions. Second, we run some "fast" scheme (such as Crank and Nicolson). We finish with pure implicit scheme. This scheme cuts of random errors.
- Parameters
-
rFast | An implementation of "fast" numerical scheme (such as Crank and Nicolson). |
rUniformSteps | This function determines the number of steps in the explicit scheme with equal weights. The number of steps in the schema equals rUniformSteps(dH) . |
rImplicitSteps | This function determines the number of steps in the implicit scheme. The number of steps in the scheme equals rImplicitSteps(dH) . |
- Returns
- Implementation of GaussRollback by a sequence of a three "rollback" operations: start with uniform explicit for smoothness, proceed with some "fast" scheme and finish with a pure implicit scheme for extra stability.
Implements the operator of conditional expectation with respect to gaussian distribution by an explicit finite difference scheme. The scheme is constructed so that all weights are almost equal to each other.
- Returns
- Implemenation of GaussRollback by means of uniform explicit finite difference scheme.
const double cfl::NGaussRollback::c_dCrankNicolsonVarStepCoeff = 0.1 |
Default value for the coefficient that determines the number of steps in the Crank and Nicolson scheme.
const double cfl::NGaussRollback::c_dImplicitVarStepCoeff = 10. |
Default value for the coefficient that determines the number of steps in the implicit scheme.
const int cfl::NGaussRollback::c_iImprovedExplicitSteps = 30 |
Default value for the number of steps of uniform explicit scheme at the beginning of the "three-layer" implementation of the operator of conditional expectation for Gaussian distribution.
const int cfl::NGaussRollback::c_iImprovedImplicitSteps = 10 |
Default value for the number of steps of implicit scheme at the end of the "three-layer" implementation of the operator of conditional expectation for Gaussian distribution.