# Cumulative Distribution Function of Sequence Generated via Random Walk

Is it possible to generically describe the CDF of a finite length random sequence generated by storing the trajectory of a random walk?

For example, assume $$X$$ is an iid random variable with the cumulative distribution function $$F_x(x)$$ , $$Y$$ is a random sequence of length $$N$$ described by $$y_{i+1} = y_i + x_i + c$$ , where $$c$$ is a constant.

I want to develop an equation of the form $$F_y(y) = func(F_x,N,c)$$ .

Is this even possible?