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<div class="title">ExtendedOrnsteinUhlenbeckProcess Class Reference<div class="ingroups"><a class="el" href="group__processes.html">Stochastic processes</a></div></div> </div>
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<!-- doxytag: class="QuantLib::ExtendedOrnsteinUhlenbeckProcess" --><!-- doxytag: inherits="QuantLib::StochasticProcess1D" -->
<p>Extended Ornstein-Uhlenbeck process class.
<a href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#details">More...</a></p>
<p><code>#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp></code></p>
<div class="dynheader">
Inheritance diagram for ExtendedOrnsteinUhlenbeckProcess:</div>
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<area shape="rect" id="node2" href="class_quant_lib_1_1_stochastic_process1_d.html" title="1-dimensional stochastic process" alt="" coords="49,6,196,37"/></map>
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<p><a href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process-members.html">List of all members.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">enum  </td><td class="memItemRight" valign="bottom"><b>Discretization</b> { <b>MidPoint</b>,
<b>Trapezodial</b>,
<b>GaussLobatto</b>
}</td></tr>
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a99abbb9639a49e4ca62d7047a6bab9a1"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::ExtendedOrnsteinUhlenbeckProcess" ref="a99abbb9639a49e4ca62d7047a6bab9a1" args="(Real speed, Volatility sigma, Real x0, const boost::function< Real(Real)> &b, Discretization discretization=MidPoint, Real intEps=1e-4)" -->
 </td><td class="memItemRight" valign="bottom"><b>ExtendedOrnsteinUhlenbeckProcess</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> speed, <a class="el" href="group__types.html#gaaa95ab7fe66935e3f7535413fad2a7d3">Volatility</a> sigma, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a89d2f497b5fd0d0a0dce2ec82c86e778">x0</a>, const boost::function< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>(<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>)> &b, Discretization <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a>=MidPoint, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> intEps=1e-4)</td></tr>
<tr><td colspan="2"><div class="groupHeader">StochasticProcess interface</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a89d2f497b5fd0d0a0dce2ec82c86e778"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::x0" ref="a89d2f497b5fd0d0a0dce2ec82c86e778" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a89d2f497b5fd0d0a0dce2ec82c86e778">x0</a> () const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the initial value of the state variable <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aab3a2b9fbc4df8e42dcf97c953347719"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::speed" ref="aab3a2b9fbc4df8e42dcf97c953347719" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>speed</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9421e902ef410ac829bb244e14b4f81b"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::volatility" ref="a9421e902ef410ac829bb244e14b4f81b" args="() const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>volatility</b> () const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a545d33724b1d6d312eb8a17f73571842"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::drift" ref="a545d33724b1d6d312eb8a17f73571842" args="(Time t, Real x) const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a545d33724b1d6d312eb8a17f73571842">drift</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the drift part of the equation, i.e. <img class="formulaInl" alt="$ \mu(t, x_t) $" src="form_360.png"/> <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab4d7fe4af7a6dd0ae710c073569821e4"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::diffusion" ref="ab4d7fe4af7a6dd0ae710c073569821e4" args="(Time t, Real x) const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#ab4d7fe4af7a6dd0ae710c073569821e4">diffusion</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const </td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. <img class="formulaInl" alt="$ \sigma(t, x_t) $" src="form_361.png"/> <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a81842299056bb82662dce099fca6bcba">expectation</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a89d2f497b5fd0d0a0dce2ec82c86e778">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#aa78ac261543c5f8c3b2e065f4a57c526">stdDeviation</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a89d2f497b5fd0d0a0dce2ec82c86e778">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#aec618e405b3e8c104f58b6616d3d482f">variance</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t0, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a89d2f497b5fd0d0a0dce2ec82c86e778">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Extended Ornstein-Uhlenbeck process class. </p>
<p>This class describes the Ornstein-Uhlenbeck process governed by </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ dx = a (b(t) - x_t) dt + \sigma dW_t. \]" src="form_135.png"/>
</p>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a81842299056bb82662dce099fca6bcba"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::expectation" ref="a81842299056bb82662dce099fca6bcba" args="(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#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a81842299056bb82662dce099fca6bcba">expectation</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">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#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">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#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>dt</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
</tr>
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<div class="memdoc">
<p>returns the expectation <img class="formulaInl" alt="$ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_362.png"/> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_354.png"/> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a8be83040b1b61f27a482f14d5b461caa">StochasticProcess1D</a>.</p>
</div>
</div>
<a class="anchor" id="aa78ac261543c5f8c3b2e065f4a57c526"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::stdDeviation" ref="aa78ac261543c5f8c3b2e065f4a57c526" args="(Time t0, Real x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#aa78ac261543c5f8c3b2e065f4a57c526">stdDeviation</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>dt</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
</tr>
</table>
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<div class="memdoc">
<p>returns the standard deviation <img class="formulaInl" alt="$ S(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_363.png"/> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_354.png"/> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a36c51f5c5f2c6dd353751857c3625ca7">StochasticProcess1D</a>.</p>
</div>
</div>
<a class="anchor" id="aec618e405b3e8c104f58b6616d3d482f"></a><!-- doxytag: member="QuantLib::ExtendedOrnsteinUhlenbeckProcess::variance" ref="aec618e405b3e8c104f58b6616d3d482f" args="(Time t0, Real x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#aec618e405b3e8c104f58b6616d3d482f">variance</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>t0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td>
<td class="paramname"><em>dt</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
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<div class="memdoc">
<p>returns the variance <img class="formulaInl" alt="$ V(x_{t_0 + \Delta t} | x_{t_0} = x_0) $" src="form_364.png"/> of the process after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_354.png"/> according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization. </p>
<p>Reimplemented from <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#ab0dfe97f905be74f88809dec0c56b998">StochasticProcess1D</a>.</p>
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