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To overcome some limits of classical neuronal models, we propose a Markoviangeneralization of the classical model based on Jacobi processes by introducingdownwards jumps to describe the activity of a single neuron. The statisticalanalysis of inter-spike intervals is performed by studying the first-passagetimes of the proposed Markovian Jacobi process with jumps through a constantboundary. In particular, we characterize its Laplace transform which isexpressed in terms of some generalization of hypergeometric functions that weintroduce, and deduce a closed-form expression for its expectation. Ourapproach, which is original in the context of first passage time problems,relies on intertwining relations between the semigroups of the classical Jacobiprocess and its generalization, which have been recently established in [11]. Anumerical investigation of the firing rate of the considered neuron isperformed for some choices of the involved parameters and of the jumpsdistributions.

Jacobi processes with jumps as neuronal models: a first passage time analysis