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Student’s t Increments

DOI: 10.4236/ojs.2016.61014, PP. 156-171

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

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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.

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