8. Consider the stochastic differential equation = x(x - 1)dN1 - ,x(x + 1)dN2 + (x2 -1) dN3 - (22 - 1) dN4 dx Suppose that x(0) E {1, 0, -1} and that the Mi are Poisson counters. Show that x evolves in the set {1, 0,-1}. If pi(t) is the probability that x(t) = 1, p2(t) is the probability that x(t) = 0 and p3(t) is the probability that x(t) = -1, and if ENi = lit, find A such that a1 1 a21 a31 p1 P1 d P2 P2 a12 a22 a32 dt a33 P3 a13 a23 P3