Author(s)

Daniel T. Cassidy

Department of Engineering Physics, McMaster University, Hamilton, Canada.

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  t increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.

Student’s t-Distribution, Truncated, Effectively Truncated, Cauchy Distribution, Random Walk, Sample Paths, Continuity

Cassidy, D. (2016) Student’s t Increments. Open Journal of Statistics, 6, 156-171. doi: 10.4236/ojs.2016.61014.