I am working on a model for time series of events with the power-law distribution of inter-event intervals. I went for a point process, governed by a stochastic differential equation

$$ d\lambda = -a \lambda^2 dt + b\eta, $$

where $\lambda$ is the intensity of the Poisson process, $a$ and $b$ are constants, $\eta \sim \text{Ber}(\lambda dt)$ is the event variable, equal to 1 if the event happens and 0 if not. The equation seems simple enough that someone must have studied it or a similar one, but do not seem to be able to find it. Any suggestions about where should look for?

PS. I am familiar with Hawkes processes, non-linear Hawkes processes, and quadratic Hawkes processes, but they are all non-local in time. Also, Hawkes processes do not give power-law distribution for inter-event intervals at all, while other models seem significantly more complex