https://doi.org/10.1140/epjb/s10051-025-01112-z
Research - Statistical and Nonlinear Physics
Continuous sample space reducing stochastic process
Department of Physics, Institute of Science, Banaras Hindu University, 221005, Varanasi, Uttar Pradesh, India
Received:
24
July
2025
Accepted:
15
December
2025
Published online:
23
December
2025
We propose a simple model for a 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 constrained multiplicative stochastic process such that the size of the state space cannot be smaller than a visibility parameter 
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 ![$$\lambda \in [0, 1].$$](/articles/epjb/abs/2025/12/10051_2025_Article_1112/10051_2025_Article_1112_tex_eq2.png)
We also examine the statistics of the size of the state space that follows a power-law distributed probability 
with a nontrivial value of the exponent as a function of the tunable parameter 
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
