  Recently, a novel framework to handle stochastic processes has emerged from a
series of studies in biology, showing situations beyond 'It\^o 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
{\alpha}-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.
