each subinterval, i.e., in place of This integral does not obey the ordinary chain rule as the Stratonovich integral does; instead one has to use the slightly more complicated Itô's lemma. Conversion between Itô and Stratonovich integrals may be performed using the formula where is any continuously differentiable function of two variables and and the last integral is an Itô integral . Langevin equations exemplify the importance of specifying the interpretation (Stratonovich or Itô) in a given problem. Suppose is a time-homogeneous Itô diffusion with continuously differentiable diffusion coefficient , i.e. it satisfies the SDE . In order to get the corresponding Stratonovich version, the term (in Itô interpretation) should translate to (in Stratonovich interpretation) as Obviously, if is independent of , the two interpretations will lead to the same form for the Langevin equation. In that case, the noise term is called "additive" (since the noise term is multiplied by only a fixed coefficient). Otherwise, if , the Langevin equation in Itô form may in general differ from that in Stratonovich form, in which case the noise term is called multiplicative (i.e., the noise is multiplied by a function of that is ). More generally, for any two semimartingales and where is the continuous part of the covariation. Stratonovich integrals in applications The Stratonovich integral lacks the important property of the Itô integral, which does not "look into the future". In many real-world applications, such as modelling stock prices, one only has information about past events, and hence the Itô interpretation is more natural. In financial mathematics the Itô interpretation is usually used. In physics, however, stochastic integrals occur as the solutions of Langevin equations. A Langevin equation is a coarse-grained version of a more microscopic model; depending on the problem in consideration, Stratonovich or Itô interpretation or even more exotic interpretations such as the isothermal interpretation, are appropriate. The Stratonovich interpretation is the most frequently used interpretation within the physical sciences. The Wong–Zakai theorem states that physical systems with non-white noise spectrum characterized by a finite noise correlation time can be approximated by a Langevin equations with white noise in Stratonovich interpretation in the limit where tends to zero. Because the Stratonovich calculus satisfies the ordinary chain rule, stochastic differential equations (SDEs) in the Stratonovich sense are more straightforward to define on differentiable manifolds, rather than just on . The tricky chain rule of the Itô calculus makes