SDEs with no strong solution arising from a problem of stochastic control
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916783074574336 |
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| author | Cox, Alexander M. G. Robinson, Benjamin A. |
| author_facet | Cox, Alexander M. G. Robinson, Benjamin A. |
| contents | We study a two-dimensional stochastic differential equation that has a unique weak solution but no strong solution. We show that this SDE shares notable properties with Tsirelson's example of a one-dimensional SDE with no strong solution. In contrast to Tsirelson's equation, which has a non-Markovian drift, we consider a strong Markov martingale with Markovian diffusion coefficient. We show that there is no strong solution of the SDE and that the natural filtration of the weak solution is generated by a Brownian motion. We also discuss an application of our results to a stochastic control problem for martingales with fixed quadratic variation in a radially symmetric environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_02519 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | SDEs with no strong solution arising from a problem of stochastic control Cox, Alexander M. G. Robinson, Benjamin A. Probability 60G44, 60H10 (Primary), 93E20 (Secondary) We study a two-dimensional stochastic differential equation that has a unique weak solution but no strong solution. We show that this SDE shares notable properties with Tsirelson's example of a one-dimensional SDE with no strong solution. In contrast to Tsirelson's equation, which has a non-Markovian drift, we consider a strong Markov martingale with Markovian diffusion coefficient. We show that there is no strong solution of the SDE and that the natural filtration of the weak solution is generated by a Brownian motion. We also discuss an application of our results to a stochastic control problem for martingales with fixed quadratic variation in a radially symmetric environment. |
| title | SDEs with no strong solution arising from a problem of stochastic control |
| topic | Probability 60G44, 60H10 (Primary), 93E20 (Secondary) |
| url | https://arxiv.org/abs/2205.02519 |