TITLE:
Student’s t Increments
AUTHORS:
Daniel T. Cassidy
KEYWORDS:
Student’s t-Distribution, Truncated, Effectively Truncated, Cauchy Distribution, Random Walk, Sample Paths, Continuity
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.1,
February
26,
2016
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 t increments should thus be useful in construction of stochastic processes and as noise driving terms in Langevin equations.