I am trying to solve a problem from Van kampens book, page 73.
A ODE is given: dx/dt = f(x). write the solution with initial values x0 and t0 in the form x = phi(x0, t - t0). Show that x obeys the defintion of the markov process with:
p1|1(x,t|x0,t0) = delta[x - phi(x0, t - t0)].
By delta, I mean the delta function. p1|1 is the transition probability.
Can anybody help me with how to start with this ?