In this section
@article{Sezik:2026:10.1098/rspa.2025.0716,
author = {Sezik, E and Knight, J and Alston, H and Roberts, C and Bertrand, T and Pruessner, G and Cocconi, L},
doi = {10.1098/rspa.2025.0716},
journal = {Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences},
pages = {1--24},
title = {Conditional splitting probabilities for hidden-state inference in drift-diffusive processes},
url = {http://dx.doi.org/10.1098/rspa.2025.0716},
volume = {482},
year = {2026}
}
TY - JOUR
AB - For a one-dimensional process in a bounded interval, splitting probabilities quantify the likelihood of exiting said interval for the first time via either boundary. For two-dimensional Markov processes (Formula presented), a joint analogue of the splitting probabilities can be defined, which captures the likelihood that the variable (Formula presented), having been initialized at (Formula presented), exits (Formula presented) for the first time via either of the interval boundaries and that the variable (Formula presented), initialized at (Formula presented), is (Formula presented) at the time of exit. Drawing on Bayes’ theorem, we introduce the related notion of conditional splitting probabilities and formalize a simple scheme that leverages them to partially infer the assumedly hidden state (Formula presented) from detecting the particle exiting at either interval boundary. We demonstrate the viability of this boundary-based inference scheme for two classes of processes (where (Formula presented) and (Formula presented) are decoupled, and where they are unidirectionally coupled with (Formula presented) depending on (Formula presented)) and argue for its broad applicability across fields concerned with the control of driven stochastic processes.
AU - Sezik,E
AU - Knight,J
AU - Alston,H
AU - Roberts,C
AU - Bertrand,T
AU - Pruessner,G
AU - Cocconi,L
DO - 10.1098/rspa.2025.0716
EP - 24
PY - 2026///
SN - 1364-5021
SP - 1
TI - Conditional splitting probabilities for hidden-state inference in drift-diffusive processes
T2 - Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
UR - http://dx.doi.org/10.1098/rspa.2025.0716
VL - 482
ER -