1111.2987 (Jianghong Shi et al.)

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

Jianghong Shi, Tianqi Chen, Ruoshi Yuan, Bo Yuan, Ping Ao

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.

View original: http://arxiv.org/abs/1111.2987