This paper establishes a new version of integration by parts formula of Markov chains for sensitivity computation, under much lower restrictions than the existing researches. Our approach is more fundamental and applicable without using Girsanov theorem or Malliavin calculus as did by past papers. Numerically, we apply this formula to compute sensitivity regarding the transition rate matrix and compare with a recent research by an IPA (infinitesimal perturbation analysis) method and other approaches.
