- Solving Stochastic DE's
This is a solution to the equation dx/dt= a*x + b*x*dW where a=b=1 and W is a wiener process. X is a process in the Stochastic linear Equation.
The solution to this SDE is exp((a-0.5*b^2)*(t)+b*W)where W is a wiener process.
- Euler approximation of SDE.
The Euler approximation of SDE is given by u(j)=u(j-1)+a*u(j-1)*dt+b*u(j-1)*dW where W is a wiener process.
Graph bellow compares the exact and approximated wiener processes.
- Solving Stochastic DE's numerically (Euller's method)
This is a numerical solution to the equation dx/dt= a*x + b*x*dW where a=b=1 and W is a wiener process. X is a process in the Stochastic linear Equation.
- Strong Convergence of the Euler's method.
- Weak Convergence of the Euler's method.
- Strong Convergence of the Milstein's higher order method.
