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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_euler_discretization.html">EulerDiscretization</a></div>
<h1>EulerDiscretization Class Reference<br>
<small>
[<a class="el" href="group__processes.html">Stochastic processes</a>]</small>
</h1><!-- doxytag: class="QuantLib::EulerDiscretization" --><!-- doxytag: inherits="QuantLib::StochasticProcess::discretization,QuantLib::StochasticProcess1D::discretization" --><code>#include <ql/processes/eulerdiscretization.hpp></code>
<p>
<div class="dynheader">
Inheritance diagram for EulerDiscretization:</div>
<div class="dynsection">
<p><center><img src="class_quant_lib_1_1_euler_discretization__inherit__graph.png" border="0" usemap="#_euler_discretization__inherit__map" alt="Inheritance graph"></center>
<map name="_euler_discretization__inherit__map">
<area shape="rect" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html" title="discretization of a stochastic process over a given time interval" alt="" coords="5,7,109,33"><area shape="rect" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html" title="discretization of a 1-D stochastic process" alt="" coords="133,7,237,33"></map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
<p>
<a href="class_quant_lib_1_1_euler_discretization-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Euler discretization for stochastic processes.
<p>
<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_array.html">Array</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_euler_discretization.html#4ccb2b71c5b53c2450145b60e512e60d">drift</a> (const <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a> &, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_euler_discretization.html#ace3fe63ebb3a6ce20936fa350225fc8">drift</a> (const <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a> &, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_euler_discretization.html#27957fdcfeb5f78298809f5f68a00049">diffusion</a> (const <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a> &, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_euler_discretization.html#2fe5ea3e1cb704f46b5feb48d6392f52">diffusion</a> (const <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a> &, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_euler_discretization.html#12f8c34783b3d11ade94edb16ec555e3">covariance</a> (const <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a> &, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_euler_discretization.html#0fb3806021f712a2284bad6a4b87b63f">variance</a> (const <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a> &, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x0, <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="4ccb2b71c5b53c2450145b60e512e60d"></a><!-- doxytag: member="QuantLib::EulerDiscretization::drift" ref="4ccb2b71c5b53c2450145b60e512e60d" args="(const StochasticProcess &, Time t0, const Array &x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
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<td class="memname"><a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a><<a class="el" href="class_quant_lib_1_1_array.html">Array</a>> drift </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a> & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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</div>
<div class="memdoc">
<p>
Returns an approximation of the drift defined as <img class="formulaInl" alt="$ \mu(t_0, \mathbf{x}_0) \Delta t $" src="form_258.png">.
<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">StochasticProcess::discretization</a>.</p>
</div>
</div><p>
<a class="anchor" name="ace3fe63ebb3a6ce20936fa350225fc8"></a><!-- doxytag: member="QuantLib::EulerDiscretization::drift" ref="ace3fe63ebb3a6ce20936fa350225fc8" args="(const StochasticProcess1D &, Time t0, Real x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> drift </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a> & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
Returns an approximation of the drift defined as <img class="formulaInl" alt="$ \mu(t_0, x_0) \Delta t $" src="form_259.png">.
<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">StochasticProcess1D::discretization</a>.</p>
</div>
</div><p>
<a class="anchor" name="27957fdcfeb5f78298809f5f68a00049"></a><!-- doxytag: member="QuantLib::EulerDiscretization::diffusion" ref="27957fdcfeb5f78298809f5f68a00049" args="(const StochasticProcess &, Time t0, const Array &x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a><<a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a>> diffusion </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a> & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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<div class="memdoc">
<p>
Returns an approximation of the diffusion defined as <img class="formulaInl" alt="$ \sigma(t_0, \mathbf{x}_0) \sqrt{\Delta t} $" src="form_260.png">.
<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">StochasticProcess::discretization</a>.</p>
</div>
</div><p>
<a class="anchor" name="2fe5ea3e1cb704f46b5feb48d6392f52"></a><!-- doxytag: member="QuantLib::EulerDiscretization::diffusion" ref="2fe5ea3e1cb704f46b5feb48d6392f52" args="(const StochasticProcess1D &, Time t0, Real x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> diffusion </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a> & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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</table>
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<div class="memdoc">
<p>
Returns an approximation of the diffusion defined as <img class="formulaInl" alt="$ \sigma(t_0, x_0) \sqrt{\Delta t} $" src="form_261.png">.
<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">StochasticProcess1D::discretization</a>.</p>
</div>
</div><p>
<a class="anchor" name="12f8c34783b3d11ade94edb16ec555e3"></a><!-- doxytag: member="QuantLib::EulerDiscretization::covariance" ref="12f8c34783b3d11ade94edb16ec555e3" args="(const StochasticProcess &, Time t0, const Array &x0, Time dt) const " -->
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<td class="memname"><a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a><<a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a>> covariance </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_stochastic_process.html">StochasticProcess</a> & </td>
<td class="paramname">, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> & </td>
<td class="paramname"> <em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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<div class="memdoc">
<p>
Returns an approximation of the covariance defined as <img class="formulaInl" alt="$ \sigma(t_0, \mathbf{x}_0)^2 \Delta t $" src="form_262.png">.
<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">StochasticProcess::discretization</a>.</p>
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<a class="anchor" name="0fb3806021f712a2284bad6a4b87b63f"></a><!-- doxytag: member="QuantLib::EulerDiscretization::variance" ref="0fb3806021f712a2284bad6a4b87b63f" args="(const StochasticProcess1D &, Time t0, Real x0, Time dt) const " -->
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<td class="memname"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> variance </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a> & </td>
<td class="paramname">, </td>
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<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>t0</em>, </td>
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<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>x0</em>, </td>
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<td class="paramtype"><a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"> <em>dt</em></td><td> </td>
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<td>)</td>
<td></td><td></td><td width="100%"> const<code> [virtual]</code></td>
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<p>
Returns an approximation of the variance defined as <img class="formulaInl" alt="$ \sigma(t_0, x_0)^2 \Delta t $" src="form_263.png">.
<p>Implements <a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">StochasticProcess1D::discretization</a>.</p>
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