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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.18086 |
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Table of Contents:
- We propose a simple model for sample space reducing (SSR) stochastic process, where the dynamical variable denoting the size of the state space is continuous. In general, one can view the model as a multiplicative stochastic process, with a constraint that the size of the state space cannot be smaller than a visibility parameter $ε$. We study the survival time statistics that reveal a subtle difference from the discrete version of the process. A straightforward generalization can explain the noisy SSR process, characterized by a tunable parameter $λ\in [0, 1]$. We also examine the statistics of the size of the state space that follows a power-law distributed probability $\mathbb{P}_ε(z\le ε) \sim z^{-α}$, with a nontrivial value of the exponent as a function of the tunable parameter $α= 1+λ$.