theta

Function of the form
$$\theta(g,h)_{p} = a_p^{-2} \int_{\R^2} |xy|^{-1-p}U_{g,h}(x,y) dxdy$$

Contains functions for simulating the linear fractional stable motion according to the algorithm developed by Mazur and Otryakhin <doi:10.32614/RJ-2020-008> based on the method from Stoev and Taqqu (2004) <doi:10.1142/S0218348X04002379>, as well as functions for estimation of parameters of these processes introduced by Mazur, Otryakhin and Podolskij (2018) <arXiv:1802.06373>, and also different related quantities.

Dmitry Otryakhin

rlfsm

Simulations and Statistical Inference for Linear Fractional
Stable Motions

Stepan Mazur

Mathias Ljungdahl

theta function

<dl><dt>p</dt>
<dd>power, real number from (-1,1)</dd>
<dt>alpha</dt>
<dd>self-similarity parameter of alpha stable random motion.</dd>
<dt>sigma</dt>
<dd>Scale parameter of lfsm</dd>
<dt>g, h</dt>
<dd>functions $g,h: \R \to \R$ with finite alpha-norm (see <code>Norm_alpha</code>).</dd></dl>

Arguments

Function theta — theta

<dl>

<dt>p</dt>
<dd>power, real number from (-1,1)</dd>


<dt>alpha</dt>
<dd>self-similarity parameter of alpha stable random motion.</dd>


<dt>sigma</dt>
<dd>Scale parameter of lfsm</dd>


<dt>g, h</dt>
<dd>functions $g,h: \R \to \R$ with finite alpha-norm (see <code>Norm_alpha</code>).</dd>

</dl>

theta: Function theta

Description

Usage

Arguments

References