# Escape noise

Two ways to introduce noise in formal spiking neuron models:

- noisy threshold(escape model or hazard model)
- noisy integration(stochastic spike arrival model or diffusion model)

In the escape model, the neuron may fire when $u<\vartheta$ the neuron may stay quiescent when $u>\vartheta$

## Escape rate and hazard function

In the escape model, spikes can occur at any time with a probability density,

Since $u$ is a function of time,$\rho$ is also time dependent,

Required condition of function $f$, when $u\rightarrow-\infty$, $f\rightarrow0$

### Example

## Interval distribution and mean fire rate

the expect value of interval distribution = $\frac{1}{mean\space fire\space rate}$ = mean period

use $\rho$ we can get interval distribution,

use $SRM_{0}$,

use non-leaky integrate-and-fire,

use leaky integrate-and-fire,

use $SRM_0$ with periodic input,we get periodic response,

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