euler1D

Simulation of the Wrapped Normal (WN) diffusion or von Mises (vM) diffusion by the Euler method in 1D, for several starting values.

Implementation of statistical methods for the estimation of
toroidal diffusions. Several diffusive models are provided, most of them
belonging to the Langevin family of diffusions on the torus. Specifically,
the wrapped normal and von Mises processes are included, which can be seen
as toroidal analogues of the Ornstein-Uhlenbeck diffusion. A collection of
methods for approximate maximum likelihood estimation, organized in four
blocks, is given: (i) based on the exact transition probability density,
obtained as the numerical solution to the Fokker-Plank equation; (ii) based
on wrapped pseudo-likelihoods; (iii) based on specific analytic
approximations by wrapped processes; (iv) based on maximum likelihood of
the stationary densities. The package allows the replicability of the
results in García-Portugués et al. (2019) <doi:10.1007/s11222-017-9790-2>.

Eduardo Portugues

sdetorus

Statistical Tools for Toroidal Diffusions

Eduardo García-Portugués

euler1D function

<dl><dt>x0</dt>
<dd>vector of length <code>nx0</code> giving the initial points.</dd>
<dt>alpha</dt>
<dd>drift parameter.</dd>
<dt>mu</dt>
<dd>mean parameter. Must be in \([\pi,\pi)\).</dd>
<dt>sigma</dt>
<dd>diffusion coefficient.</dd>
<dt>N</dt>
<dd>number of discretization steps.</dd>
<dt>delta</dt>
<dd>discretization step.</dd>
<dt>type</dt>
<dd>integer giving the type of diffusion. Currently, only <code>1</code> for WN and <code>2</code> for vM are supported.</dd>
<dt>maxK</dt>
<dd>maximum absolute value of the windings considered in the computation of the WN.</dd>
<dt>expTrc</dt>
<dd>truncation for exponential: <code>exp(x)</code> with <code>x &lt;= -expTrc</code> is set to zero. Defaults to <code>30</code>.</dd></dl>

Arguments

Simulation of trajectories of the WN or vM diffusion in 1D — euler1D

<dl>

<dt>x0</dt>
<dd>vector of length <code>nx0</code> giving the initial points.</dd>


<dt>alpha</dt>
<dd>drift parameter.</dd>


<dt>mu</dt>
<dd>mean parameter. Must be in \([\pi,\pi)\).</dd>


<dt>sigma</dt>
<dd>diffusion coefficient.</dd>


<dt>N</dt>
<dd>number of discretization steps.</dd>


<dt>delta</dt>
<dd>discretization step.</dd>


<dt>type</dt>
<dd>integer giving the type of diffusion. Currently, only <code>1</code> for WN and <code>2</code> for vM are supported.</dd>


<dt>maxK</dt>
<dd>maximum absolute value of the windings considered in the computation of the WN.</dd>


<dt>expTrc</dt>
<dd>truncation for exponential: <code>exp(x)</code> with <code>x &lt;= -expTrc</code> is set to zero. Defaults to <code>30</code>.</dd>

</dl>

euler1D: Simulation of trajectories of the WN or vM diffusion in 1D

Description

Usage

Value

Arguments

Examples