# What kind of stochastic process could this be?

I have been studying the fascinating subject of stochastic processes and have constructed various equations I can think of and then I try to look up literature for that process.

One process I have thought of is this:

$$dS = f(s,t)dt + \alpha N(t)\,dt$$

Here $$f(s,t)$$ is a deterministic function and $$N(t)$$ is a simple random walk consisting of step functions representing the count of all increment/decrement events upto $$t$$. Is this a standard class of processes that I can read up on?

The closest thing I have been able to find are jump-diffusion-drift models but these are not quite what I have, as my process involves the time integration of the stochastic process $$N(t)$$ which is in continuous time but has discrete state space.