Martingale Problem and Quadratic Family

Assuming uniqueness of the martingale problem for Markov processes of generators qₜ in a quadratic family like \[q_t(i,j) = a_t(i) q_0(i,j)^2 + b_t(i) q_0(i,j) - a_t(i)/N ∑_k q_0(i,k)^2,\] where aₜ(i),bₜ(i) are predictable processes, N is the number of states, and q₀ represents the generator of a stationary reference Markov process which satisfies q₀(i,j)>0 for all $i,j$, we obtain the sufficient and necessary conditions for the Girsanov transformation.