marian::ForwardKolmogorowEquation Class Reference
Class implements Forward Kolmogorow Equation. More...
#include <forwardKolmogorovEq.hpp>
Public Member Functions | |
| ForwardKolmogorowEquation (ConvectionDiffusion process) | |
| constructor | |
| std::vector< double > | solve (SmartPointer< FDScheme > scheme, std::vector< double > init, std::vector< SmartPointer< BoundaryCondition > > bcs, std::vector< double > spatial_grid, std::vector< double > time_grid) |
| Solves forward equation. More... | |
| std::vector< double > | solveAndSave (SmartPointer< FDScheme > scheme, std::vector< double > init, std::vector< SmartPointer< BoundaryCondition > > bcs, std::vector< double > spatial_grid, std::vector< double > time_grid, std::string file_name) |
| Solves equation and save it to CSV file. More... | |
| TridiagonalOperator | getOperator (const std::vector< double > &sgrid) |
| Constructs the discretized linear operator for Forward Kolmogorow Equation in form of Tridiagonal operator. More... | |
Private Attributes | |
| ConvectionDiffusion | process_ |
| Stochastic process. | |
Detailed Description
Forward Kolmogorow Equation arise in the theory of continuous-time continuous-state Markov processes. Let's assume that the physical system state x(t) evolves according to the stochastic differential equation
![\[ dx(t)=\mu dt+\sigma dW(t)\]](form_1.png)
then probability distribution p(t,x) of x is governed by the Kolmogorov forward equation
![\[\frac{d p(t,x)}{dt} = \Big(\frac{1}{2}\sigma^2 \frac{\partial^2 }{\partial x^2} - \mu \frac{\partial }{\partial x}\Big) p(t,x) \]](form_5.png)
This class is used to construct the PDE basing on diffusion process and solve it using finite difference method.
- Examples:
- FokkerPlanckEqExample.cpp.
Member Function Documentation
| TridiagonalOperator marian::ForwardKolmogorowEquation::getOperator | ( | const std::vector< double > & | spatial_grid | ) |
The operator is given as:
![\[\hat{L} = \frac{1}{2}\sigma^2 \frac{\partial^2 }{\partial x^2} - \mu \frac{\partial^2 }{\partial x} \]](form_4.png)
| std::vector< double > marian::ForwardKolmogorowEquation::solve | ( | SmartPointer< FDScheme > | scheme, |
| std::vector< double > | init, | ||
| std::vector< SmartPointer< BoundaryCondition > > | bcs, | ||
| std::vector< double > | spatial_grid, | ||
| std::vector< double > | time_grid | ||
| ) |
- Parameters
-
scheme Differential scheme init Initial value bcs Boundary conditions spatial_grid Spatial grid used to discretize the system time_grid Time grid used to discretize the system
- Returns
- Solution in form of std::vector
| std::vector< double > marian::ForwardKolmogorowEquation::solveAndSave | ( | SmartPointer< FDScheme > | scheme, |
| std::vector< double > | init, | ||
| std::vector< SmartPointer< BoundaryCondition > > | bcs, | ||
| std::vector< double > | spatial_grid, | ||
| std::vector< double > | time_grid, | ||
| std::string | file_name | ||
| ) |
- Parameters
-
scheme Differential scheme init Initial value bcs Boundary conditions spatial_grid Spatial grid used to discretize the system time_grid Time grid used to discretize the system file_name CSV file name
- Returns
- Solution in form of std::vector
The documentation for this class was generated from the following files:
- C:/Unix/home/OEM/fdm/src/diffusion/forwardKolmogorovEq.hpp
- C:/Unix/home/OEM/fdm/src/diffusion/forwardKolmogorovEq.cpp
