Itô’s Formula and Stochastic Differential Equations

Given a stochastic process (V t ) t≥0 having trajectories with bounded variation and a sufficiently regular function f, it is possible to define the integral of Z t = f(V t ) with respect to dV t as follows $$ \int_0^t {Z_s dV_s = \int_0^t {f\left( {V_s } \right)dV_s } } , $$ (5.1) i.e. in the sense of a Riemann-Stieltjes integral.