Analog study of the first passage time problem driven by power-law distributed noise

In this work, we develop an analog circuit to generate a stochastic signal with stationary distribution exhibiting a tunable power-law tail. The proposed circuit design is a variant of a recently introduced one based on a differential equation with both multiplicative and additive noises. Here, the circuit is carefully designed in order to ensure that all components operate within their specific regimes. We provide a detailed characterization of the output signal, including the power-law exponent dependence on the tunable component. We apply the present circuit to study the first passage time problem in a simple integrate-fire model of neural dynamics driven by a non-Gaussian noise.