Student’s <i>t</i> Increments

Abstract

Some moments and limiting properties of independent Student’s t increments are studied. Inde-pendent Student’s t 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 t -distributions are continuous. Sample paths for Student’s t -distributions are also continuous. Student’s <i>t</i> increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.