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Student’s t Increments


Affiliations
1 Department of Engineering Physics, McMaster University, Hamilton, Canada
 

Some moments and limiting properties of independent Student's t increments are studied. Independent Student's t increments are independent draws from not-truncated, truncated, and effectively truncated Student's t-distributions with shape parameters ν ≥ 1 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 ν ≥ 3 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.

Keywords

Student's t-Distribution, Truncated, Effectively Truncated, Cauchy Distribution, Random Walk, Sample Paths, Continuity.
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  • Student’s t Increments

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Authors

Daniel T. Cassidy
Department of Engineering Physics, McMaster University, Hamilton, Canada

Abstract


Some moments and limiting properties of independent Student's t increments are studied. Independent Student's t increments are independent draws from not-truncated, truncated, and effectively truncated Student's t-distributions with shape parameters ν ≥ 1 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 ν ≥ 3 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.

Keywords


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