The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation
The most probable transition paths (MPTPs) of a stochastic dynamical system are the global minimisers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange (EL) equation (a second-order differential equation with initial-termina...
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| Format: | Journal Article |
| Language: | English |
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2024
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| Online Access: | https://hdl.handle.net/10356/173096 |
| _version_ | 1811693709271498752 |
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| author | Huang, Yuanfei Huang, Qiao Duan, Jinqiao |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Huang, Yuanfei Huang, Qiao Duan, Jinqiao |
| author_sort | Huang, Yuanfei |
| collection | NTU |
| description | The most probable transition paths (MPTPs) of a stochastic dynamical system are the global minimisers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange (EL) equation (a second-order differential equation with initial-terminal conditions) from a variational principle. This work is devoted to showing a sufficient and necessary characterisation for the MPTPs of stochastic dynamical systems with Brownian noise. We prove that, under appropriate conditions, the MPTPs are completely determined by a first-order ordinary differential equation. The equivalence is established by showing that the Onsager-Machlup action functional of the original system can be derived from the corresponding Markovian bridge process. For linear stochastic systems and the nonlinear Hongler’s model, the first-order differential equations determining the MPTPs are shown analytically to imply the EL equations of the Onsager-Machlup functional. For general nonlinear systems, the determining first-order differential equations can be approximated, in a short time or for the small noise case. Some numerical experiments are presented to illustrate our results. |
| first_indexed | 2024-10-01T06:55:59Z |
| format | Journal Article |
| id | ntu-10356/173096 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:55:59Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1730962024-01-15T15:35:45Z The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation Huang, Yuanfei Huang, Qiao Duan, Jinqiao School of Physical and Mathematical Sciences Science::Mathematics Stochastic Dynamical Systems Most Probable Transition Paths The most probable transition paths (MPTPs) of a stochastic dynamical system are the global minimisers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange (EL) equation (a second-order differential equation with initial-terminal conditions) from a variational principle. This work is devoted to showing a sufficient and necessary characterisation for the MPTPs of stochastic dynamical systems with Brownian noise. We prove that, under appropriate conditions, the MPTPs are completely determined by a first-order ordinary differential equation. The equivalence is established by showing that the Onsager-Machlup action functional of the original system can be derived from the corresponding Markovian bridge process. For linear stochastic systems and the nonlinear Hongler’s model, the first-order differential equations determining the MPTPs are shown analytically to imply the EL equations of the Onsager-Machlup functional. For general nonlinear systems, the determining first-order differential equations can be approximated, in a short time or for the small noise case. Some numerical experiments are presented to illustrate our results. Submitted/Accepted version The work of Y Huang is partly supported by the NSFC Grants 11531006 and 11771449. Y Huang also would like to thank the support from his research group in the National University of Singapore during his postdoctoral period. The work of Q Huang is supported by FCT, Portugal, Project PTDC/MAT-STA/28812/2017. 2024-01-11T08:12:59Z 2024-01-11T08:12:59Z 2024 Journal Article Huang, Y., Huang, Q. & Duan, J. (2024). The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation. Nonlinearity, 37(1), 015010-. https://dx.doi.org/10.1088/1361-6544/ad0ffe 0951-7715 https://hdl.handle.net/10356/173096 10.1088/1361-6544/ad0ffe 2-s2.0-85180109062 1 37 015010 en Nonlinearity © 2023 IOP Publishing Ltd & London Mathematical Society. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1088/1361-6544/ad0ffe. application/pdf |
| spellingShingle | Science::Mathematics Stochastic Dynamical Systems Most Probable Transition Paths Huang, Yuanfei Huang, Qiao Duan, Jinqiao The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation |
| title | The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation |
| title_full | The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation |
| title_fullStr | The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation |
| title_full_unstemmed | The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation |
| title_short | The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation |
| title_sort | most probable transition paths of stochastic dynamical systems a sufficient and necessary characterisation |
| topic | Science::Mathematics Stochastic Dynamical Systems Most Probable Transition Paths |
| url | https://hdl.handle.net/10356/173096 |
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