We discuss the main features of a stochastic model for the firing activity of a neuronal unit, proposed in Di Crescenzo and Martinucci (2007). The neuronal membrane potential is described by a stochastic process defined as $$ V(t)=v_0 \,\exp\left\{-\nu t+ \sum_{k=1}^{N(t)} Z_k \right\}, \quad t>0, \qquad V(0)=v_0, $$ where $N(t)$ is a Poisson process counting the number of excitatory stimuli received by the neuron, and $\{Z_k\}$ is a sequence of exponentially distributed random variables. The cases of constant and linearly increasing arrival rate of neuronal stimuli are treated. Attention is given mainly to the firing density, that is the first-passage-time density of $V(t)$ through an upper constant threshold, which is expressed in terms of a suitable series
A review of a stochastic neuronal model with jumps driven by Poisson process
DI CRESCENZO, Antonio;MARTINUCCI, BARBARA
2008
Abstract
We discuss the main features of a stochastic model for the firing activity of a neuronal unit, proposed in Di Crescenzo and Martinucci (2007). The neuronal membrane potential is described by a stochastic process defined as $$ V(t)=v_0 \,\exp\left\{-\nu t+ \sum_{k=1}^{N(t)} Z_k \right\}, \quad t>0, \qquad V(0)=v_0, $$ where $N(t)$ is a Poisson process counting the number of excitatory stimuli received by the neuron, and $\{Z_k\}$ is a sequence of exponentially distributed random variables. The cases of constant and linearly increasing arrival rate of neuronal stimuli are treated. Attention is given mainly to the firing density, that is the first-passage-time density of $V(t)$ through an upper constant threshold, which is expressed in terms of a suitable seriesI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
