[size=1em]Recently, a novel framework to handle stochastic processes has emerged from a series of studies in biology, showing situations beyond 'It versus Stratonovich'. Its internal consistency can be demonstrated via the zero mass limit of a generalized Klein–Kramers equation. Moreover, the connection to other integrations becomes evident: the obtained Fokker–Planck equation defines a new type of stochastic calculus that in general differs from the α-type interpretation. A unique advantage of this new approach is a natural correspondence between stochastic and deterministic dynamics, which is useful or may even be essential in practice. The core of the framework is a transformation from the usual Langevin equation to a form that contains a potential function with two additional dynamical matrices, which reveals an underlying symplectic structure. The framework has a direct physical meaning and a straightforward experimental realization. A recent experiment has offered a first empirical validation of this new stochastic integration.

• Beyond It versus Stratonovich

  [size=1.2em]Ruoshi Yuan and Ping Ao J. Stat. Mech. (2012) P07010