Pathwise Shrinkage and Probabilistic Calibration of the Multiplicative Half-Cauchy Process

Siddhesh Kulkarni
10/15/2026
stat.MEcs.LGmath.PR

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Abstract

We characterize the multiplicative half-Cauchy process through its log-scale random-walk representation, establishing shrinkage, expansion, and critical regimes, almost-sure summability, local rebounds, and effective dimension. We also derive a semi-analytic calibration rule linking interpretable prior probability statements to its scale parameter.

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Cite this paper

@article{kulkarni2026pathwise,
  title  = {Pathwise Shrinkage and Probabilistic Calibration of the Multiplicative Half-Cauchy Process},
  author = {Siddhesh Kulkarni},
  year   = {2026},
  eprint = {2610.21136},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2610.21136v1}
}

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