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arXiv · 1203.6600

Beyond Itô versus Stratonovich

Ruoshi Yuan·Ping Ao
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Abstract

Recently, a novel framework to handle stochastic processes has emerged from a series of studies in biology, showing situations beyond 'Itô 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.

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BibTeXRIS

Ruoshi Yuan, Ping Ao. 2012-09-14. Beyond Itô versus Stratonovich. https://doi.org/10.1088/1742-5468%2F2012%2F07%2Fp07010

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