Hey neptunhiker.

You might try representing y as a function of time and x as a function of time for some region of time T.

If you define y(t) = 0 as no event occutring at time t and y(t) = 1 as an event occurring at time t, then you can say that

y(t) = H(x(t)) where H(t) = 0 if t <= 0 and H(t) = 1 if t > 0.

Then using this, you define y(t) as the condition of an event happening at time t which may be discrete or continuous.