Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.13508 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We consider a dynamic system that is driven by an intensity-modulated Poisson process with intensity $Λ(t)=λ(t)+\varepsilonν(t)$. We derive an exact relation between the input-output cross-correlation in the spontaneous state ($\varepsilon=0$) and the linear response to the modulation ($\varepsilon>0$). If $\varepsilon$ is sufficiently small, linear response theory captures the full response. The relation can be regarded as a variant of the Furutsu-Novikov theorem for the case of shot noise. As we show, the relation is still valid in the presence of additional independent noise. Furthermore, we derive an extension to Cox-process input, which provides an instance of colored shot noise. We discuss applications to particle detection and to neuroscience. Using the new relation, we obtain a fluctuation-response-relation for a leaky integrate-and-fire neuron. We also show how the new relation can be used in a remote control problem in a recurrent neural network. The relations are numerically tested for both stationary and non-stationary dynamics. Lastly, extensions to marked Poisson processes and to higher-order statistics are presented.