1203.6600 (Ruoshi Yuan et al.)

Beyond Ito vs. Stratonovich    [PDF]

Ruoshi Yuan, Ping Ao

Recently, a novel framework to handle stochastic processes emerges from a series of studies in biology, showing situations beyond "Ito vs. 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 a 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. Indeed, a recent experiment offers a first empirical validation of such new stochastic integration.

View original: http://arxiv.org/abs/1203.6600