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<li class="navelem"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html">StochasticProcess1D</a> </li>
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<!-- doxytag: class="QuantLib::StochasticProcess1D" --><!-- doxytag: inherits="QuantLib::StochasticProcess" -->
<p>1-dimensional stochastic process
<a href="class_quant_lib_1_1_stochastic_process1_d.html#details">More...</a></p>
<p><code>#include <ql/stochasticprocess.hpp></code></p>
<div class="dynheader">
Inheritance diagram for StochasticProcess1D:</div>
<div class="dyncontent">
<div class="center"><img src="class_quant_lib_1_1_stochastic_process1_d__inherit__graph.png" border="0" usemap="#_stochastic_process1_d_inherit__map" alt="Inheritance graph"/></div>
<map name="_stochastic_process1_d_inherit__map" id="_stochastic_process1_d_inherit__map">
<area shape="rect" id="node5" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html" title="Extended Ornstein-Uhlenbeck process class." alt="" coords="392,5,627,35"/><area shape="rect" id="node7" href="class_quant_lib_1_1_forward_measure_process1_d.html" title="forward-measure 1-D stochastic process" alt="" coords="419,58,600,89"/><area shape="rect" id="node9" href="class_quant_lib_1_1_geman_roncoroni_process.html" title="Geman-Roncoroni process class." alt="" coords="424,111,595,142"/><area shape="rect" id="node11" href="class_quant_lib_1_1_generalized_black_scholes_process.html" title="Generalized Black-Scholes stochastic process." alt="" coords="400,165,619,195"/><area shape="rect" id="node13" href="class_quant_lib_1_1_generalized_ornstein_uhlenbeck_process.html" title="Piecewise linear Ornstein-Uhlenbeck process class." alt="" coords="385,218,633,249"/><area shape="rect" id="node15" href="class_quant_lib_1_1_geometric_brownian_motion_process.html" title="Geometric brownian-motion process." alt="" coords="399,271,620,302"/><area shape="rect" id="node17" href="class_quant_lib_1_1_hull_white_process.html" title="Hull-White stochastic process." alt="" coords="447,325,572,355"/><area shape="rect" id="node19" href="class_quant_lib_1_1_merton76_process.html" title="Merton-76 jump-diffusion process." alt="" coords="448,378,571,409"/><area shape="rect" id="node21" href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html" title="Ornstein-Uhlenbeck process class." alt="" coords="420,431,599,462"/><area shape="rect" id="node23" href="class_quant_lib_1_1_square_root_process.html" title="Square-root process class." alt="" coords="440,485,579,515"/><area shape="rect" id="node25" href="class_quant_lib_1_1_variance_gamma_process.html" title="Variance gamma process." alt="" coords="427,538,592,569"/><area shape="rect" id="node2" href="class_quant_lib_1_1_stochastic_process.html" title="multi-dimensional stochastic process class." alt="" coords="7,271,137,302"/></map>
<center><span class="legend">[<a href="graph_legend.html">legend</a>]</span></center></div>
<p><a href="class_quant_lib_1_1_stochastic_process1_d-members.html">List of all members.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="nested-classes"></a>
Classes</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html">discretization</a></td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">discretization of a 1-D stochastic process <a href="class_quant_lib_1_1_stochastic_process1_d_1_1discretization.html#details">More...</a><br/></td></tr>
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">1-D stochastic process interface</div></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ac02c619851c7c95e6a7f08a284c568b0"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::x0" ref="ac02c619851c7c95e6a7f08a284c568b0" args="() const =0" -->
virtual <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_stochastic_process1_d.html#ac02c619851c7c95e6a7f08a284c568b0">x0</a> () const =0</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="a6bded8896a46fad4d189950552432cd3"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::drift" ref="a6bded8896a46fad4d189950552432cd3" args="(Time t, Real x) const =0" -->
virtual <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_stochastic_process1_d.html#a6bded8896a46fad4d189950552432cd3">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 =0</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) $" src="form_360.png"/> <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="afaf479da3baa52185b369071b1689d89"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::diffusion" ref="afaf479da3baa52185b369071b1689d89" args="(Time t, Real x) const =0" -->
virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#afaf479da3baa52185b369071b1689d89">diffusion</a> (<a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> t, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> x) const =0</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">returns the diffusion part of the equation, i.e. <img class="formulaInl" alt="$ \sigma(t, x_t) $" src="form_361.png"/> <br/></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">virtual <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_stochastic_process1_d.html#a8be83040b1b61f27a482f14d5b461caa">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_stochastic_process1_d.html#ac02c619851c7c95e6a7f08a284c568b0">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">virtual <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_stochastic_process1_d.html#a36c51f5c5f2c6dd353751857c3625ca7">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_stochastic_process1_d.html#ac02c619851c7c95e6a7f08a284c568b0">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">virtual <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_stochastic_process1_d.html#ab0dfe97f905be74f88809dec0c56b998">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_stochastic_process1_d.html#ac02c619851c7c95e6a7f08a284c568b0">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">virtual <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_stochastic_process1_d.html#a690ddf2804c6862d281f9181bd2b633e">evolve</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_stochastic_process1_d.html#ac02c619851c7c95e6a7f08a284c568b0">x0</a>, <a class="el" href="group__types.html#ga14fb8fca43a68f4168654e1f9f7e22f7">Time</a> dt, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> dw) const </td></tr>
<tr><td class="memItemLeft" align="right" valign="top">virtual <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_stochastic_process1_d.html#a905bb2d5a924e5274035b0850c3e04fb">apply</a> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#ac02c619851c7c95e6a7f08a284c568b0">x0</a>, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> dx) const </td></tr>
<tr><td colspan="2"><h2><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a704996c48f48a23c4db6a6549a094807"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::StochasticProcess1D" ref="a704996c48f48a23c4db6a6549a094807" args="(const boost::shared_ptr< discretization > &)" -->
 </td><td class="memItemRight" valign="bottom"><b>StochasticProcess1D</b> (const boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a> > &)</td></tr>
<tr><td colspan="2"><h2><a name="pro-attribs"></a>
Protected Attributes</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aea3658beebc66268a48cf5273cce6abd"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::discretization_" ref="aea3658beebc66268a48cf5273cce6abd" args="" -->
boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_stochastic_process_1_1discretization.html">discretization</a> > </td><td class="memItemRight" valign="bottom"><b>discretization_</b></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>1-dimensional stochastic process </p>
<p>This class describes a stochastic process governed by </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. \]" src="form_350.png"/>
</p>
</div><hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="a8be83040b1b61f27a482f14d5b461caa"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::expectation" ref="a8be83040b1b61f27a482f14d5b461caa" args="(Time t0, Real x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a8be83040b1b61f27a482f14d5b461caa">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>
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</table>
</div>
<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 in <a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#a81842299056bb82662dce099fca6bcba">HullWhiteForwardProcess</a>, <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a81842299056bb82662dce099fca6bcba">GeneralizedBlackScholesProcess</a>, <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#a81842299056bb82662dce099fca6bcba">ExtendedOrnsteinUhlenbeckProcess</a>, <a class="el" href="class_quant_lib_1_1_generalized_ornstein_uhlenbeck_process.html#a81842299056bb82662dce099fca6bcba">GeneralizedOrnsteinUhlenbeckProcess</a>, <a class="el" href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html#a81842299056bb82662dce099fca6bcba">OrnsteinUhlenbeckProcess</a>, and <a class="el" href="class_quant_lib_1_1_hull_white_process.html#a81842299056bb82662dce099fca6bcba">HullWhiteProcess</a>.</p>
</div>
</div>
<a class="anchor" id="a36c51f5c5f2c6dd353751857c3625ca7"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::stdDeviation" ref="a36c51f5c5f2c6dd353751857c3625ca7" args="(Time t0, Real x0, Time dt) const " -->
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a36c51f5c5f2c6dd353751857c3625ca7">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>
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<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
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<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 in <a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#aa78ac261543c5f8c3b2e065f4a57c526">HullWhiteForwardProcess</a>, <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#aa78ac261543c5f8c3b2e065f4a57c526">ExtendedOrnsteinUhlenbeckProcess</a>, <a class="el" href="class_quant_lib_1_1_geman_roncoroni_process.html#aa78ac261543c5f8c3b2e065f4a57c526">GemanRoncoroniProcess</a>, <a class="el" href="class_quant_lib_1_1_generalized_ornstein_uhlenbeck_process.html#aa78ac261543c5f8c3b2e065f4a57c526">GeneralizedOrnsteinUhlenbeckProcess</a>, <a class="el" href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html#aa78ac261543c5f8c3b2e065f4a57c526">OrnsteinUhlenbeckProcess</a>, and <a class="el" href="class_quant_lib_1_1_hull_white_process.html#aa78ac261543c5f8c3b2e065f4a57c526">HullWhiteProcess</a>.</p>
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<a class="anchor" id="ab0dfe97f905be74f88809dec0c56b998"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::variance" ref="ab0dfe97f905be74f88809dec0c56b998" args="(Time t0, Real x0, Time dt) const " -->
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<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#ab0dfe97f905be74f88809dec0c56b998">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>
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<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x0</em>, </td>
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<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>
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<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 in <a class="el" href="class_quant_lib_1_1_hull_white_forward_process.html#aec618e405b3e8c104f58b6616d3d482f">HullWhiteForwardProcess</a>, <a class="el" href="class_quant_lib_1_1_ornstein_uhlenbeck_process.html#aec618e405b3e8c104f58b6616d3d482f">OrnsteinUhlenbeckProcess</a>, <a class="el" href="class_quant_lib_1_1_extended_ornstein_uhlenbeck_process.html#aec618e405b3e8c104f58b6616d3d482f">ExtendedOrnsteinUhlenbeckProcess</a>, <a class="el" href="class_quant_lib_1_1_generalized_ornstein_uhlenbeck_process.html#aec618e405b3e8c104f58b6616d3d482f">GeneralizedOrnsteinUhlenbeckProcess</a>, and <a class="el" href="class_quant_lib_1_1_hull_white_process.html#aec618e405b3e8c104f58b6616d3d482f">HullWhiteProcess</a>.</p>
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<a class="anchor" id="a690ddf2804c6862d281f9181bd2b633e"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::evolve" ref="a690ddf2804c6862d281f9181bd2b633e" args="(Time t0, Real x0, Time dt, Real dw) const " -->
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<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a690ddf2804c6862d281f9181bd2b633e">evolve</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>
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<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>
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<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>
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<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>dw</em> </td>
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<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
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<p>returns the asset value after a time interval <img class="formulaInl" alt="$ \Delta t $" src="form_354.png"/> according to the given discretization. By default, it returns </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w \]" src="form_365.png"/>
</p>
<p> where <img class="formulaInl" alt="$ E $" src="form_358.png"/> is the expectation and <img class="formulaInl" alt="$ S $" src="form_212.png"/> the standard deviation. </p>
<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#a28916b3498be74dceb699ad1499a46c0">GeneralizedBlackScholesProcess</a>, <a class="el" href="class_quant_lib_1_1_geman_roncoroni_process.html#a28916b3498be74dceb699ad1499a46c0">GemanRoncoroniProcess</a>, and <a class="el" href="class_quant_lib_1_1_extended_black_scholes_merton_process.html#a28916b3498be74dceb699ad1499a46c0">ExtendedBlackScholesMertonProcess</a>.</p>
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<a class="anchor" id="a905bb2d5a924e5274035b0850c3e04fb"></a><!-- doxytag: member="QuantLib::StochasticProcess1D::apply" ref="a905bb2d5a924e5274035b0850c3e04fb" args="(Real x0, Real dx) const " -->
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<td class="memname">virtual <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> <a class="el" href="class_quant_lib_1_1_stochastic_process1_d.html#a905bb2d5a924e5274035b0850c3e04fb">apply</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>x0</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"><em>dx</em> </td>
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<td></td>
<td>)</td>
<td></td><td> const<code> [virtual]</code></td>
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<p>applies a change to the asset value. By default, it returns <img class="formulaInl" alt="$ x + \Delta x $" src="form_366.png"/>. </p>
<p>Reimplemented in <a class="el" href="class_quant_lib_1_1_generalized_black_scholes_process.html#aee1aadb67f9085eb8a9fc89604bd8ead">GeneralizedBlackScholesProcess</a>, and <a class="el" href="class_quant_lib_1_1_merton76_process.html#a556c2d99ae77d13156c6371c4faaf960">Merton76Process</a>.</p>
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