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<html>
<head>
<title>
SDE - Stochastic Differential Equations
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SDE <br> Stochastic Differential Equations
</h1>
<hr>
<p>
<b>SDE</b>
is a FORTRAN90 library which
illustrates the properties of stochastic differential equations and some
algorithms for handling them,
by Desmond Higham.
</p>
<p>
The library requires access to the QR_SOLVE library as well.
</p>
<p>
The original version of these routines is available at
<a href = "http://www.maths.strath.ac.uk/~aas96106/algfiles.html">
"http://www.maths.strath.ac.uk/~aas96106/algfiles.html".</a>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SDE</b> is available in
<a href = "../../c_src/sde/sde.html">a C version</a> and
<a href = "../../cpp_src/sde/sde.html">a C++ version</a> and
<a href = "../../f77_src/sde/sde.html">a FORTRAN77 version</a> and
<a href = "../../f_src/sde/sde.html">a FORTRAN90 version</a> and
<a href = "../../m_src/sde/sde.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/black_scholes/black_scholes.html">
BLACK_SCHOLES</a>,
a FORTRAN90 library which
implements some simple approaches to
the Black-Scholes option valuation theory,
by Desmond Higham.
</p>
<p>
<a href = "../../m_src/brownian_motion_simulation/brownian_motion_simulation.html">
BROWNIAN_MOTION_SIMULATION</a>,
a MATLAB program which
simulates Brownian motion in an M-dimensional region.
</p>
<p>
<a href = "../../m_src/cnoise/cnoise.html">
CNOISE</a>,
a MATLAB library which
generates samples of noise obeying a 1/f^alpha power law,
by Miroslav Stoyanov.
</p>
<p>
<a href = "../../f_src/colored_noise/colored_noise.html">
COLORED_NOISE</a>,
a FORTRAN90 library which
generates samples of noise obeying a 1/f^alpha power law.
</p>
<p>
<a href = "../../f_src/correlation/correlation.html">
CORRELATION</a>,
a FORTRAN90 library which
contains examples of statistical correlation functions.
</p>
<p>
<a href = "../../examples/gnuplot/gnuplot.html">
GNUPLOT</a>,
examples which
illustrate the use of the gnuplot graphics program.
</p>
<p>
<a href = "../../f_src/pce_burgers/pce_burgers.html">
PCE_BURGERS</a>,
a FORTRAN90 program which
defines and solves a version of the time-dependent viscous Burgers equation,
with uncertain viscosity, using a polynomial chaos expansion in terms
of Hermite polynomials,
by Gianluca Iaccarino.
</p>
<p>
<a href = "../../m_src/pce_legendre/pce_legendre.html">
PCE_LEGENDRE</a>,
a MATLAB program which
assembles the system matrix associated with a polynomal chaos expansion
of a 2D stochastic PDE, using Legendre polynomials;
</p>
<p>
<a href = "../../f_src/pce_ode_hermite/pce_ode_hermite.html">
PCE_ODE_HERMITE</a>,
a FORTRAN90 program which
sets up a simple scalar ODE for exponential decay with an uncertain
decay rate, using a polynomial chaos expansion in terms of Hermite polynomials.
</p>
<p>
<a href = "../../f_src/pink_noise/pink_noise.html">
PINK_NOISE</a>,
a FORTRAN90 library which
computes a "pink noise" signal obeying a 1/f power law.
</p>
<p>
<a href = "../../f_src/qr_solve/qr_solve.html">
QR_SOLVE</a>,
a FORTRAN90 library which
computes the least squares solution of a linear system A*x=b.
</p>
<p>
<a href = "../../m_src/stochastic_diffusion/stochastic_diffusion.html">
STOCHASTIC_DIFFUSION</a>,
MATLAB functions which
implement several versions of a stochastic diffusivity coefficient.
</p>
<p>
<a href = "../../m_src/stochastic_gradient_nd_noise/stochastic_gradient_nd_noise.html">
STOCHASTIC_GRADIENT_ND_NOISE</a>,
a MATLAB program which
solves an optimization problem involving a functional over a system
with stochastic noise.
</p>
<p>
<a href = "../../f_src/stochastic_rk/stochastic_rk.html">
STOCHASTIC_RK</a>,
a FORTRAN90 library which
applies a Runge Kutta (RK) scheme to a stochastic differential equation.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Original MATLAB version by Desmond Higham.
FORTRAN90 version by John Burkardt.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Desmond Higham,<br>
An Algorithmic Introduction to Numerical Simulation of
Stochastic Differential Equations,<br>
SIAM Review,<br>
Volume 43, Number 3, September 2001, pages 525-546.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sde.f90">sde.f90</a>, the source code.
</li>
<li>
<a href = "sde.sh">sde.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sde_prb.f90">sde_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sde_prb.sh">sde_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "sde_prb_output.txt">sde_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
The calling program creates various data and command files which
can be used with GNUPLOT to create images.
<ul>
<li>
<a href = "bpath_commands.txt">bpath_commands.txt</a>,
commands to plot the data from BPATH.
</li>
<li>
<a href = "bpath_data.txt">bpath_data.txt</a>,
data from BPATH.
</li>
<li>
<a href = "bpath.png">bpath.png</a>,
a plot of the BPATH data.
</li>
<li>
<a href = "bpath_average_commands.txt">bpath_average_commands.txt</a>,
commands to plot the data from BPATH_AVERAGE.
</li>
<li>
<a href = "bpath_average_data.txt">bpath_average_data.txt</a>,
data from BPATH_AVERAGE.
</li>
<li>
<a href = "bpath_average.png">bpath_average.png</a>,
a plot of the BPATH_AVERAGE data.
</li>
<li>
<a href = "chain_commands.txt">chain_commands.txt</a>,
commands to plot the data from CHAIN.
</li>
<li>
<a href = "chain_data.txt">chain_data.txt</a>,
data from CHAIN.
</li>
<li>
<a href = "chain.png">chain.png</a>,
a plot of the CHAIN data.
</li>
<li>
<a href = "em_commands.txt">em_commands.txt</a>,
commands to plot the data from EM.
</li>
<li>
<a href = "em1_data.txt">em1_data.txt</a>,
data from EM.
</li>
<li>
<a href = "em2_data.txt">em2_data.txt</a>,
data from EM.
</li>
<li>
<a href = "em.png">em.png</a>,
a plot of the EM data.
</li>
<li>
<a href = "emstrong_commands.txt">emstrong_commands.txt</a>,
commands to plot the data from EMSTRONG.
</li>
<li>
<a href = "emstrong_data.txt">emstrong_data.txt</a>,
data from EMSTRONG.
</li>
<li>
<a href = "emstrong.png">emstrong.png</a>,
a plot of the EMSTRONG data.
</li>
<li>
<a href = "emweak0_commands.txt">emweak0_commands.txt</a>,
commands to plot the data from EMWEAK with the standard EM method.
</li>
<li>
<a href = "emweak0_data.txt">emweak0_data.txt</a>,
data from EMWEAK with the standard EM method.
</li>
<li>
<a href = "emweak0.png">emweak0.png</a>,
a plot of the data from EMWEAK with the standard EM method.
</li>
<li>
<a href = "emweak1_commands.txt">emweak1_commands.txt</a>,
commands to plot the data from EMWEAK with the weak EM method.
</li>
<li>
<a href = "emweak1_data.txt">emweak1_data.txt</a>,
data from EMWEAK with the weak EM method.
</li>
<li>
<a href = "emweak1.png">emweak1.png</a>,
a plot of the data from EMWEAK with the weak EM method.
</li>
<li>
<a href = "milstrong_commands.txt">milstrong_commands.txt</a>,
commands to plot the MILSTRONG data.
</li>
<li>
<a href = "milstrong_data.txt">milstrong_data.txt</a>,
data from MILSTRONG.
</li>
<li>
<a href = "milstrong.png">milstrong.png</a>,
a plot of the strong convergence data from MILSTRONG.
</li>
<li>
<a href = "stab_asymptotic_commands.txt">stab_asymptotic_commands.txt</a>,
commands to plot the STAB_ASYMPTOTIC data.
</li>
<li>
<a href = "stab_asymptotic_data1.txt">stab_asymptotic_data1.txt</a>,
data from STAB_ASYMPTOTIC.
</li>
<li>
<a href = "stab_asymptotic_data2.txt">stab_asymptotic_data2.txt</a>,
data from STAB_ASYMPTOTIC.
</li>
<li>
<a href = "stab_asymptotic_data3.txt">stab_asymptotic_data3.txt</a>,
data from STAB_ASYMPTOTIC.
</li>
<li>
<a href = "stab_asymptotic.png">stab_asymptotic.png</a>,
a plot of the asymptotic stability results from STAB_ASYMPTOTIC.
</li>
<li>
<a href = "stab_meansquare_commands.txt">stab_meansquare_commands.txt</a>,
commands to plot the STAB_MEANSQUARE data.
</li>
<li>
<a href = "stab_meansquare_data1.txt">stab_meansquare_data1.txt</a>,
data from STAB_MEANSQUARE.
</li>
<li>
<a href = "stab_meansquare_data2.txt">stab_meansquare_data2.txt</a>,
data from STAB_MEANSQUARE.
</li>
<li>
<a href = "stab_meansquare_data3.txt">stab_meansquare_data3.txt</a>,
data from STAB_MEANSQUARE.
</li>
<li>
<a href = "stab_meansquare.png">stab_meansquare.png</a>,
a plot of the meansquare stability results from STAB_MEANSQUARE.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BPATH</b> performs a Brownian path simulation.
</li>
<li>
<b>BPATH_AVERAGE:</b> displays the average of 1000 Brownian paths.
</li>
<li>
<b>BPATH_AVERAGE_GNUPLOT</b> writes a GNUPLOT input file to plot BPATH_AVERAGE data.
</li>
<li>
<b>BPATH_GNUPLOT</b> writes a GNUPLOT input file to plot BPATH data.
</li>
<li>
<b>CHAIN</b> tests the stochastic Chain Rule.
</li>
<li>
<b>CHAIN_GNUPLOT</b> writes a GNUPLOT input file to plot CHAIN data.
</li>
<li>
<b>EM</b> applies the Euler-Maruyama method to a linear SDE.
</li>
<li>
<b>EM_GNUPLOT</b> writes a GNUPLOT input file to plot EM data.
</li>
<li>
<b>EMSTRONG</b> tests the strong convergence of the EM method.
</li>
<li>
<b>EMSTRONG_GNUPLOT</b> writes a GNUPLOT input file to plot EMSTRONG data.
</li>
<li>
<b>EMWEAK</b> tests the weak convergence of the Euler-Maruyama method.
</li>
<li>
<b>EMWEAK_GNUPLOT</b> writes a GNUPLOT input file to plot EMWEAK data.
</li>
<li>
<b>FILENAME_INC</b> increments a partially numeric filename.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>MILSTRONG</b> tests the strong convergence of the Milstein method.
</li>
<li>
<b>MILSTRONG_GNUPLOT</b> writes a GNUPLOT input file to plot MILSTRONG data.
</li>
<li>
<b>R8_NORMAL_01</b> returns a unit pseudonormal R8.
</li>
<li>
<b>R8_SIGN</b> returns the sign of an R8.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_NORMAL_01</b> returns a unit pseudonormal R8MAT.
</li>
<li>
<b>R8VEC_MEAN</b> returns the mean of an R8VEC.
</li>
<li>
<b>R8VEC_NORMAL_01</b> returns a unit pseudonormal R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>STAB_ASYMPTOTIC</b> examines asymptotic stability.
</li>
<li>
<b>STAB_MEANSQUARE</b> examines mean-square stability.
</li>
<li>
<b>STOCHASTIC_INTEGRAL_ITO</b> approximates the Ito integral of W(t) dW.
</li>
<li>
<b>STOCHASTIC_INTEGRAL_STRAT</b> approximates the Stratonovich integral of W(t) dW.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 21 September 2012.
</i>
<!-- John Burkardt -->
</body>
</html>