Relation of Biologically Motivated New Interpretation of Stochastic Differential Equations to Ito Process

Details Relation of Biologically Motivated New Interpretation of Stochastic Differential Equations to Ito Process Relation of Biologically Motivated New Interpretation of Stochastic Differential Equations to Ito Process

2011-11-13

arxiv.org/abs/1111.2987v1

Physics

Mathematical Physics

15 pages, 2 figures

Scientific paper

Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed. Different interpretations specify different dynamics. Recently, a special biologically motivated interpretation of SDE is put forward by one of us. This construction shows the existence of potential function for general processes, which reveals both local and global dynamics. Despite its powerful property, its relation with classical ones in arbitrary dimension remains obscure. In this paper, we discuss different interpretations of SDE and derive the relation between the new interpretation and Ito process. We end with a question for readers.

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