We consider two different scenarios for a particle  moving in R.

1. Symmetrical but not homogeneous: From timet to t+ , the particle moves from x to the right with probability R(x) and to the left with probability L(x) = R(x) and does not move with probability N(x) = 1-R(x)-L(x).

2. Homogeneous but not symmetrical: From time t to t+, the particle moves to the right with probability R and to the left with probability L = 1-R= R.

For each scenario, give and justify the equation for u(t+,x), and then  take the parabolic limit. What are the resulting equations? (non-symmetrical case, you need to make an assumption for this to work. What is it?)