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

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 (at equal potential energy) 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 possibility of an outbreak is higher even if the process starts with a small initial bias toward 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 the mean, which is 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.