Given $$f(x) = a_0 + a_1\,x + a_2\,x^2 + \dots + a_p\,x^p$$ $$g(x) = b_0 + b_1\,x + b_2\,x^2 + \dots + b_q\,x^q$$
Is there any conclusion about the strong solution for following SDE: $$dX_t = f(X_t)\,dt + g(X_t)\,dW_t$$
Most results I found require drift and diffusion coefficients are Lipschitz...
Thank you very much!