Feller diffusion in an interval: Inhomogeneous fluctuation-induced asymmetric escape

Prashanta Bauri; Debasish Mondal

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arXiv · 2607.07649

Feller diffusion in an interval: Inhomogeneous fluctuation-induced asymmetric escape

Prashanta Bauri·Debasish Mondal

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Abstract

We present an inhomogeneous fluctuation-induced asymmetric escape event of a Feller diffusion confined to a finite interval with two competing absorbing boundaries. The dynamics correspond to an overdamped Brownian motion in a shifted harmonic potential with state-dependent diffusivity. We set two exit points (equal potential energies), equidistant from the potential minima: an extinction site near the origin and an outbreak point. The multiplicative fluctuations are suppressed near the extinction boundary, biasing trajectories toward the outbreak state. The mean exit time exhibits a non-monotonic dependence on the initial condition and the drift-to-noise strength ratio, attaining a maximum when the particle is initialized toward the extinction (low-noise) site. The outbreak possibility is more likely even if the process started with a small initial bias towards the low-noise boundary. The spatial location of the lowest coefficient of variation (CV) is nicely corroborated by the maximum exit time, which is the hallmark of a stochastic escape from an interval. The fluctuation in escape time is found to dominate its mean as a non-trivial function of the drift-to-noise strength and the initial spatial bias. The observed asymmetries in escape also shape the speed-accuracy trade-off in stochastic decision-making events.

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Prashanta Bauri, Debasish Mondal. 2026-07-08. Feller diffusion in an interval: Inhomogeneous fluctuation-induced asymmetric escape. https://arxiv.org/abs/2607.07649

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