Probability Flow Approach to the Onsager--Machlup Functional for Jump-Diffusion Processes Article Swipe
Yuanfei Huang
,
Xiang Zhou
,
Jinqiao Duan
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.01340
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.01340
The Onsager--Machlup action functional is an important concept in statistical mechanics and thermodynamics to describe the probability of fluctuations in nonequilibrium systems. It provides a powerful tool for analyzing and predicting the behavior of complex stochastic systems. For diffusion process, the path integral method and the Girsanov transformation are two main approaches to construct the Onsager--Machlup functional. However, it is a long-standing challenge to apply these two methods to the jump-diffusion process, because the complexity of jump noise presents intrinsic technical barriers to derive the Onsager--Machlup functional. In this work, we propose a new strategy to solve this problem by utilizing the equivalent probabilistic flow between the pure diffusion process and the jump-diffusion process. For the first time, we rigorously establish the closed-form expression of the Onsager--Machlup functional for jump-diffusion processes with finite jump activity, which include an important term of the Lévy intensity at the origin. The same probability flow approach is further applied to the Lévy process with infinite jump activity, and yields a time-discrete version of the Onsager--Machlup functional.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2409.01340
- https://arxiv.org/pdf/2409.01340
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4402954575
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- OpenAlex ID
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https://openalex.org/W4402954575Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2409.01340Digital Object Identifier
- Title
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Probability Flow Approach to the Onsager--Machlup Functional for Jump-Diffusion ProcessesWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-09-02Full publication date if available
- Authors
-
Yuanfei Huang, Xiang Zhou, Jinqiao DuanList of authors in order
- Landing page
-
https://arxiv.org/abs/2409.01340Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2409.01340Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2409.01340Direct OA link when available
- Concepts
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Jump, Statistical physics, Jump diffusion, Flow (mathematics), Diffusion, Mechanics, Mathematics, Physics, Thermodynamics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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