Back to Search
Start Over
Most probable transition paths in piecewise-smooth stochastic differential equations
- Source :
- Physica D 439 (2022) 133424
- Publication Year :
- 2021
-
Abstract
- We develop a path integral framework for determining most probable paths in a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin-Wentzell theory of large deviations to cases where the system is piecewise-smooth and may be non-autonomous. In particular, we consider an $n-$dimensional system with a switching manifold in the drift that forms an $(n-1)-$dimensional hyperplane and investigate noise-induced transitions between metastable states on either side of the switching manifold. To do this, we mollify the drift and use $\Gamma-$convergence to derive an appropriate rate functional for the system in the piecewise-smooth limit. The resulting functional consists of the standard Freidlin-Wentzell rate functional, with an additional contribution due to times when the most probable path slides in a crossing region of the switching manifold. We explore implications of the derived functional through two case studies, which exhibit notable phenomena such as non-unique most probable paths and noise-induced sliding in a crossing region.<br />Comment: 38 pages, 9 figures
- Subjects :
- Mathematics - Dynamical Systems
Mathematics - Probability
37H10, 37J45
Subjects
Details
- Database :
- arXiv
- Journal :
- Physica D 439 (2022) 133424
- Publication Type :
- Report
- Accession number :
- edsarx.2112.12958
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.physd.2022.133424