Probabilistic Construction of Lagrangean of Diffusion Process and Its Application
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概要
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Lagrangean (Onsager-Machlup function) is rigorously obtained for a diffusion process in Euclidean space by first introducing the probability measure in `path space' and then evaluating the the measure of neighbourhood of a smooth path. Consequently probabilistic meaning of the detailed balance and the cyclic balance is clarified. On the basis of this probabilistic clarification and the global definitions of the detailed balance and of the cyclic balance, these two balances are successfully characterized with the help of the notions `vorticity' and `circulation' in fluid mechanics. Discussed is the transformation property of the Stratonovich type stochastic differential equation as well as of the Lagrangean given by Stratonovich. and it is shown that neither is covariant in general, contrary to the recent argument by Graham.
- 理論物理学刊行会の論文
- 1978-03-25
著者
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ITO Hidemi
Department of Internal Medicine and Molecular Science, Nagoya City University, Graduate School of Me
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ITO Hitoshi
Department of Physics, Faculty of Science and Engineering, Kinki University
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ITO Hiroaki
Department of Physics, Nagoya University
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ITO Hidemi
Department of Physics, Kyoto University
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