eerstepassageeffect

The eerstepassageeffect is a proposed phenomenon in stochastic dynamics where an observable undergoes a pronounced, step-like change during the first passage of a stochastic process across a prescribed threshold. It is described as the abrupt response that accompanies a threshold crossing in noisy systems, rather than a gradual transition.

Origin and terminology: The name derives from the Dutch phrase eerste passage, meaning first passage. The concept is used in discussions of threshold-driven responses and first-passage phenomena and is not universally standardized across disciplines. Different authors may describe the effect in slightly different terms or within different modeling frameworks.

Theoretical framework: In a typical diffusion model dX = μ dt + σ dW_t with an absorbing boundary θ, the first-passage time T_θ = inf{t ≥ 0: X(t) crosses θ}. The eerstepassageeffect refers to a step-like component in a measured quantity Y(t) that is tied to the crossing event, often appearing near t ≈ T_θ. A simple representation is Y(t) ≈ y0 + Δy · P(T_θ ≤ t), which yields an abrupt transition whose sharpness depends on noise level and the choice of threshold.

Applications and examples: The concept appears in discussions of neuronal firing (threshold membrane potential triggering a spike), chemical kinetics (rapid product release upon surpassing a critical concentration), and other threshold-driven processes in physics, biology, and engineering where first-passage events govern observed responses.

Limitations and status: The term is not a universally adopted standard in the literature. Identification of the eerstepassageeffect depends on clear threshold definitions, careful handling of stochastic variability, and disentangling the effect from other nonlinear or measurement-related factors.

See also: First-passage time, threshold models, stochastic processes, hitting probability.