Warning! |

More in detail, the user can specify:

- the Itô or the Stratonovich SDE to be simulated. This can be a user defined SDE or an SDE chosen from the

- the SDE structural parameter values;

- the number of the SDE's solution trajectories to be simulated;

- the numerical integration method (Euler-Maruyama or Milstein);

- the time interval [

- the integration stepsize;

- the parameter estimation method;

to obtain (see also the screenshots):

- parameter estimates and confidence intervals;

- plot(s) of the solution trajectories;

- plot(s) of the trajectories empirical mean, together with their 95% confidence bands and the 1st and 3rd quartiles;

- histogram(s) of the trajectories distribution at the endtime

- Monte-Carlo statistics of the solution process at the endtime

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Only MATLAB base is required to run the toolbox.

From a numerical point of view, users are highly encouraged in giving a look into the References section, in particular the excellent monographies [1,2] and the article [3], the latter giving a MATLAB-based introduction to SDE simulation. Other useful references for numerical methods are [4,5,6,7]. Highly specialistic references for SDE theory and stochastic calculus are [8,9,10,11]; important references for parameter estimation of diffusion processes are [12,13]. See also the Toolbox User's Guide and references therein.

Take a look at the pdf User's Guide (~3.4 Mb). I suggest to download it (click the right mouse button and select "save target as") instead of open it with a browser.

This program is free software (read the License); however if you have used it in your researches and if you have published any results, please give me credit and cite my work as:

Umberto Picchini.

Furthermore you are encouraged to send me a corresponding reprint.

Copyright (C) 2007-2018, Umberto Picchini.

Early versions of this toolbox have been created with the support of the Biomathematics Laboratory at the Institute for Systems Analysis and Informatics "A. Ruberti", organ of the Italian National Research Council (CNR); though, possible bugs, errors and misprints are on my own responsibility.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

[1] Peter E. Kloeden and Eckhard Platen. Numerical solution of stochastic differential equations. Springer, 1992.

[2] Peter E. Kloeden, Eckhard Platen and Henri Schurz. Numerical solution of SDE through computer experiments. Springer, 1994.

[3] Desmond J. Higham. An algorithmic introduction to numerical simulation of stochastic differential equations.

[4] K. Burrage and P.M. Burrage. High strong order explicit Runge–Kutta methods for stochastic ordinary differential equations.

[5] P.M. Burrage and K. Burrage. A variable stepsize implementation for stochastic differential equations.

[6] Pamela Marion Burrage. Runge–Kutta methods for stochastic differential equations. PhD thesis, Department of Mathematics, University of Queensland (Australia), 1999. http://www.maths.uq.edu.au/~kb/pam.ps

[7] Andreas Rößler. Runge–Kutta methods for the numerical solution of stochastic differential equations. PhD thesis, Department of Mathematics, University of Darmstadt, 2003.

[8] Ioannis Karatzas and Steven E. Shreve. Brownian motion and stochastic calculus. Springer- Verlag, 1991.

[9] Bernt Øksendal. Stochastic differential equations: an introduction with applications. Springer, second edition, 2000.

[10] L.C.G. Rogers and David Williams. Diffusions, Markov processes and martingales. Volume 2: Itô calculus. John Wiley & Sons, 1987.

[11] D.W. Stroock and S.R.S. Varadhan. Multidimensional Diffusion Processes. Springer-Verlag, 1979.

[12] B.L.S. Prakasa Rao. Statistical Inference for Diffusion Type Processes. Arnold, London and Oxford University press, New York, 1999.

[13] Y.A. Kutoyants. Statistical Inference for Ergodic Diffusion Processes. Springer, London, 2004.