Particle exchange Monte Carlo methods for eigenfunction and related nonlinear problems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915459054436352 |
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| author | Dupuis, Paul Zhang, Benjamin J. |
| author_facet | Dupuis, Paul Zhang, Benjamin J. |
| contents | We introduce and develop a novel particle exchange Monte Carlo method. Whereas existing methods apply to eigenfunction problems where the eigenvalue is known (e.g., integrals with respect to a Gibbs measure, which can be interpreted as corresponding to eigenvalue zero), here the focus is on problems where the eigenvalue is not known a priori. To obtain an appropriate particle exchange rule we must consider a pair of processes, with one evolving forward in time and the other backward. Applications to eigenfunction problems corresponding to quasistationary distributions and ergodic stochastic control are discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_23456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Particle exchange Monte Carlo methods for eigenfunction and related nonlinear problems Dupuis, Paul Zhang, Benjamin J. Numerical Analysis Computation We introduce and develop a novel particle exchange Monte Carlo method. Whereas existing methods apply to eigenfunction problems where the eigenvalue is known (e.g., integrals with respect to a Gibbs measure, which can be interpreted as corresponding to eigenvalue zero), here the focus is on problems where the eigenvalue is not known a priori. To obtain an appropriate particle exchange rule we must consider a pair of processes, with one evolving forward in time and the other backward. Applications to eigenfunction problems corresponding to quasistationary distributions and ergodic stochastic control are discussed. |
| title | Particle exchange Monte Carlo methods for eigenfunction and related nonlinear problems |
| topic | Numerical Analysis Computation |
| url | https://arxiv.org/abs/2505.23456 |