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  Here we provide links to free software which can be used in concert with ANISE.

Normally Distributed Random Numbers

A good free program called 'drnor.f' can be downloaded from the GAMS website at gams.nist.gov/serve.cgi/Module/NMS/DRNOR/11308/. Alternatively, 'gasdev.f' and 'ran2.f' are good programs available commercially from Numerical Recipes (www.nr.com).

Generating Colored Noise

Colored noise can be generated using ANISE as described in the documentation. For many complex noises $V_t$ with correlation functions

\begin{eqnarray}\html{eqn0} M[V_t^*V_s]&=&\alpha (t-s)\nonumber \end{eqnarray}


it is possible to represent the correlation function as a sum of exponentials

\begin{eqnarray}\html{eqn0} \alpha(t)=\sum_{j=1}^m A_j e^{-\gamma_j t} e^{i\omega_j t}\nonumber \end{eqnarray}


with positive coefficients $A_j$ and decay rates $\gamma_j$. It is then relatively simple to generate the colored noise $V_t$ from $V_t=\sum_j\mu_t^j$ where $ \mu_{t}^{j}$ obey \begin{eqnarray}\html{eqn0} d\mu_t^j&=&-(\gamma_j-i\omega_j)\mu_t^j dt+A_j\sqrt{2\gamma_j} dW_t^j\nonumber \end{eqnarray}


where $W_t^j$ is a complex Wiener process satisfying \begin{eqnarray}\html{eqn0} M[dW_t^{j*} dW_s^j]&=&\delta_{t,s}dt\nonumber \\ M[dW_t^j dW_s^j]&=&0.\nonumber \end{eqnarray}


Note that one must integrate from some large negative time until the first time of interest since

\begin{eqnarray}\html{eqn0} \mu_t^j&=&A_j\sqrt{2\gamma_j} e^{i\omega_j t}\int_{-\infty}^t e^{-\gamma_j (t-s)}dW_s^j.\nonumber \end{eqnarray}


Usually the only difficulty is finding the parameters of the decomposition.

Here we provide a free least squares fortran program corrfit.f which generates a set of optimal parameters when provided with the number m, data for $\alpha(t)$, and some bounds on the parameters.

If corrfit.f should fail to give converged parameters, another program 'harminv' may work better and it is also freely available at ab-initio.mit.edu/harminv/.

Fortran Code for Test Examples

Click above for codes for math and finance test examples. You will need the programs gasdev.f and ran2.f from Numerical Recipes (www.nr.com).

C Code for Test Examples

Click above for codes for math and finance test examples. You will need the programs gasdev.c and ran2.c from Numerical Recipes (www.nr.com).

Other Free SDE Software

Click above for a set of free stochastic differential equation integrators. We do not recommend that they be used for situations in which high accuracy solutions are required.


* Innovative Stochastic Algorithms *


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