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In this paper, we present a mathematical description for excitable biological membranes, in particular neuronal membranes. We aim to model the (spatio-) temporal dynamics, e.g., the travelling of an action potential along the axon, subject to noise, such as ion channel noise. Using the framework of Piecewise Deterministic Processes (PDPs) we provide an… (More)

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic… (More)

In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to… (More)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete random events are globally coupled with continuous… (More)

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