期刊
JOURNAL OF STATISTICAL PHYSICS
卷 148, 期 3, 页码 579-590出版社
SPRINGER
DOI: 10.1007/s10955-012-0532-8
关键词
Stochastic differential equation; Boltzmann-Gibbs distribution; Fokker-Planck equation; Potential function
资金
- National 973 Project [2010CB529200]
- Natural Science Foundation of China [NFSC91029738, NFSC61073087]
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 new interpretation of SDE is put forward by one of us. This interpretation has a built-in Boltzmann-Gibbs distribution and 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 will clarify such connection and derive the concise relation between the new interpretation and Ito process. We point out that the derived relation is experimentally testable.
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