Another mathematical ambiguity occurs for Langevin equations with multiplicative noise, which refers to noise terms that are multiplied by a non-constant function of the dependent variables, e.g., . If a multiplicative noise is intrinsic to the system, its definition is ambiguous, as it is equally valid to interpret it according to Stratonovich- or Ito- scheme (see Itô calculus). Nevertheless, physical observables are independent of the interpretation, provided the latter is applied consistently when manipulating the equation. This is necessary because the symbolic rules of calculus differ depending on the interpretation scheme. If the noise is external to the system, the appropriate interpretation is the Stratonovich one.
Another mathematical ambiguity occurs for Langevin equations with multiplicative noise, which refers. to noise terms that are multiplied by a non-constant function of the dependent variables, e.g., . If a multiplicative noise is intrinsic to the system, its definition is ambiguous, as it i?s equally valid to interpret it according to Stratonovich- or Ito- scheme (see Itô calculus). Nevertheless, physical observables are independent of the interpretation, provided the latter is applied consistently when manipulating the equation. Thi.s is necessary because the symbolic rules of calculus differ depending on the interpretation scheme. If the noise is extern:al to the system, the appropriate interpretation is the Stratonovich one.