Optimal State Equation for the Control of a Diffusion with Two Distinct Dynamics
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909166691418112 |
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| author | Chen, Zengjing Wu, Panyu Zhou, Xiaowen |
| author_facet | Chen, Zengjing Wu, Panyu Zhou, Xiaowen |
| contents | We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether it takes values bigger or smaller than a threshold value. Adopting a perturbation type approach, we find an expression for potential measure of the optimal state process. We then obtain an expression for the transition density of the optimal state process by inverting the associated Laplace transform. Properties including the stationary distribution of the optimal state process are discussed. Finally, the expression of the value function is given for this class stochastic control problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07618 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal State Equation for the Control of a Diffusion with Two Distinct Dynamics Chen, Zengjing Wu, Panyu Zhou, Xiaowen Optimization and Control 93E20, 60J60, 60G17 We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether it takes values bigger or smaller than a threshold value. Adopting a perturbation type approach, we find an expression for potential measure of the optimal state process. We then obtain an expression for the transition density of the optimal state process by inverting the associated Laplace transform. Properties including the stationary distribution of the optimal state process are discussed. Finally, the expression of the value function is given for this class stochastic control problems. |
| title | Optimal State Equation for the Control of a Diffusion with Two Distinct Dynamics |
| topic | Optimization and Control 93E20, 60J60, 60G17 |
| url | https://arxiv.org/abs/2404.07618 |