%0 Journal Article
%T Student¡¯s <i>t</i> Increments
%A Daniel T. Cassidy
%J Open Journal of Statistics
%P 156-171
%@ 2161-7198
%D 2016
%I Scientific Research Publishing
%R 10.4236/ojs.2016.61014
%X Some moments and limiting properties of independent Student¡¯s <i>t</i> increments are studied. Inde-pendent Student¡¯s <i>t</i> increments are independent draws from not-truncated, truncated, and effectively truncated Student¡¯s t-distributions with shape parameters and can be used to create random walks. It is found that sample paths created from truncated and effectively truncated Student¡¯s <i>t</i>-distributions are continuous. Sample paths for Student¡¯s <i>t</i>-distributions are also continuous. Student¡¯s &nbsp;&lt;i&gt;t&lt;/i&gt; increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.
%K Student¡¯s &lt
%K i&gt
%K t&lt
%K /i&gt
%K -Distribution
%K Truncated
%K Effectively Truncated
%K Cauchy Distribution
%K Random Walk
%K Sample Paths
%K Continuity
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=63852