Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 148, Issue 3, Pages 579-590Publisher
SPRINGER
DOI: 10.1007/s10955-012-0532-8
Keywords
Stochastic differential equation; Boltzmann-Gibbs distribution; Fokker-Planck equation; Potential function
Categories
Funding
- National 973 Project [2010CB529200]
- Natural Science Foundation of China [NFSC91029738, NFSC61073087]
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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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